LMFDB - Embedded newform 546.2.bz.b.73.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			73.2
Character	$\chi$	$=$	546.73
Dual form			546.2.bz.b.187.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99820 - 0.535417i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.718636 + 2.54628i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99820 - 0.535417i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.718636 + 2.54628i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.03435 - 1.79154i) q^{10} +(0.490864 + 1.83193i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.43996 + 2.65454i) q^{13} +(-2.64552 + 0.0351224i) q^{14} +(-1.46279 - 1.46279i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.24802 - 2.16164i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(0.714132 + 0.191351i) q^{19} +(1.46279 + 1.46279i) q^{20} +(-0.650785 + 2.56446i) q^{21} -1.89655 q^{22} +(-7.35489 + 4.24635i) q^{23} +(0.965926 - 0.258819i) q^{24} +(-0.623983 - 0.360257i) q^{25} +(-1.93258 - 3.04387i) q^{26} +1.00000i q^{27} +(0.650785 - 2.56446i) q^{28} -8.10492 q^{29} +(1.79154 - 1.03435i) q^{30} +(1.93801 + 7.23277i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.490864 + 1.83193i) q^{33} +(1.76497 + 1.76497i) q^{34} +(-0.0726574 - 5.47276i) q^{35} -1.00000i q^{36} +(2.96249 + 0.793796i) q^{37} +(-0.369662 + 0.640273i) q^{38} +(-3.44034 + 1.07892i) q^{39} +(-1.79154 + 1.03435i) q^{40} +(0.895842 - 0.895842i) q^{41} +(-2.30865 - 1.29234i) q^{42} +10.4587i q^{43} +(0.490864 - 1.83193i) q^{44} +(-0.535417 - 1.99820i) q^{45} +(-2.19807 - 8.20332i) q^{46} +(0.482703 - 1.80147i) q^{47} +1.00000i q^{48} +(-5.96712 + 3.65970i) q^{49} +(0.509480 - 0.509480i) q^{50} +(2.16164 - 1.24802i) q^{51} +(3.44034 - 1.07892i) q^{52} +(2.70278 - 4.68135i) q^{53} +(-0.965926 - 0.258819i) q^{54} -3.92339i q^{55} +(2.30865 + 1.29234i) q^{56} +(0.522781 + 0.522781i) q^{57} +(2.09771 - 7.82875i) q^{58} +(12.9998 - 3.48328i) q^{59} +(0.535417 + 1.99820i) q^{60} +(8.23336 - 4.75353i) q^{61} -7.48791 q^{62} +(-1.84583 + 1.89550i) q^{63} -1.00000i q^{64} +(6.29683 - 3.99791i) q^{65} +(-1.64246 - 0.948277i) q^{66} +(8.60990 - 2.30701i) q^{67} +(-2.16164 + 1.24802i) q^{68} -8.49270 q^{69} +(5.30509 + 1.34627i) q^{70} +(-4.51316 - 4.51316i) q^{71} +(0.965926 + 0.258819i) q^{72} +(0.693968 - 0.185948i) q^{73} +(-1.53350 + 2.65609i) q^{74} +(-0.360257 - 0.623983i) q^{75} +(-0.522781 - 0.522781i) q^{76} +(-4.31186 + 2.56637i) q^{77} +(-0.151729 - 3.60236i) q^{78} +(4.82081 + 8.34988i) q^{79} +(-0.535417 - 1.99820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.633456 + 1.09718i) q^{82} +(1.63597 - 1.63597i) q^{83} +(1.84583 - 1.89550i) q^{84} +(-3.65119 + 3.65119i) q^{85} +(-10.1024 - 2.70692i) q^{86} +(-7.01907 - 4.05246i) q^{87} +(1.64246 + 0.948277i) q^{88} +(-0.868177 + 3.24008i) q^{89} +2.06869 q^{90} +(-8.51266 - 4.30519i) q^{91} +8.49270 q^{92} +(-1.93801 + 7.23277i) q^{93} +(1.61516 + 0.932511i) q^{94} +(-1.32453 - 0.764717i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-1.08804 + 1.08804i) q^{97} +(-1.99060 - 6.71100i) q^{98} +(-1.34107 + 1.34107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.99820	−	0.535417i	−0.893624	−	0.239446i	−0.217348	−	0.976094i	$-0.569741\pi$
$5$	−1.99820	−	0.535417i	−0.893624	−	0.239446i	−0.676276	+	0.736649i	$0.736407\pi$
$6$	−0.707107	+	0.707107i	−0.288675	+	0.288675i
$7$	0.718636	+	2.54628i	0.271619	+	0.962405i
$7$	0.718636	+	2.54628i	0.271619	+	0.962405i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.03435	−	1.79154i	0.327089	−	0.566535i
$11$	0.490864	+	1.83193i	0.148001	+	0.552348i	0.999603	+	0.0281594i	$0.00896460\pi$
$11$	0.490864	+	1.83193i	0.148001	+	0.552348i	−0.851602	+	0.524188i	$0.824369\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−2.43996	+	2.65454i	−0.676724	+	0.736237i
$13$	−2.43996	+	2.65454i	−0.676724	+	0.736237i
$14$	−2.64552	+	0.0351224i	−0.707044	+	0.00938685i
$15$	−1.46279	−	1.46279i	−0.377690	−	0.377690i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.24802	−	2.16164i	0.302690	−	0.524275i	−0.674054	−	0.738682i	$-0.735449\pi$
$17$	1.24802	−	2.16164i	0.302690	−	0.524275i	0.976744	+	0.214407i	$0.0687819\pi$
$18$	−0.965926	+	0.258819i	−0.227671	+	0.0610042i
$19$	0.714132	+	0.191351i	0.163833	+	0.0438989i	0.339803	−	0.940497i	$-0.389640\pi$
$19$	0.714132	+	0.191351i	0.163833	+	0.0438989i	−0.175970	+	0.984396i	$0.556306\pi$
$20$	1.46279	+	1.46279i	0.327089	+	0.327089i
$21$	−0.650785	+	2.56446i	−0.142013	+	0.559612i
$22$	−1.89655			−0.404347
$23$	−7.35489	+	4.24635i	−1.53360	+	0.885425i	−0.534410	+	0.845225i	$0.679466\pi$
$23$	−7.35489	+	4.24635i	−1.53360	+	0.885425i	−0.999192	+	0.0401997i	$0.987201\pi$
$24$	0.965926	−	0.258819i	0.197169	−	0.0528312i
$25$	−0.623983	−	0.360257i	−0.124797	−	0.0720513i
$26$	−1.93258	−	3.04387i	−0.379010	−	0.596952i
$27$			1.00000i			0.192450i
$28$	0.650785	−	2.56446i	0.122987	−	0.484638i
$29$	−8.10492			−1.50505			−0.752523	−	0.658566i	$-0.771163\pi$
$29$	−8.10492			−1.50505			−0.752523	+	0.658566i	$0.771163\pi$
$30$	1.79154	−	1.03435i	0.327089	−	0.188845i
$31$	1.93801	+	7.23277i	0.348078	+	1.29904i	0.888975	+	0.457955i	$0.151418\pi$
$31$	1.93801	+	7.23277i	0.348078	+	1.29904i	−0.540898	+	0.841089i	$0.681915\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	−0.490864	+	1.83193i	−0.0854485	+	0.318898i
$34$	1.76497	+	1.76497i	0.302690	+	0.302690i
$35$	−0.0726574	−	5.47276i	−0.0122813	−	0.925066i
$36$		−	1.00000i		−	0.166667i
$37$	2.96249	+	0.793796i	0.487030	+	0.130499i	0.493974	−	0.869477i	$-0.335544\pi$
$37$	2.96249	+	0.793796i	0.487030	+	0.130499i	−0.00694419	+	0.999976i	$0.502210\pi$
$38$	−0.369662	+	0.640273i	−0.0599671	+	0.103866i
$39$	−3.44034	+	1.07892i	−0.550895	+	0.172765i
$40$	−1.79154	+	1.03435i	−0.283267	+	0.163544i
$41$	0.895842	−	0.895842i	0.139907	−	0.139907i	−0.633685	−	0.773592i	$-0.718458\pi$
$41$	0.895842	−	0.895842i	0.139907	−	0.139907i	0.773592	+	0.633685i	$0.218458\pi$
$42$	−2.30865	−	1.29234i	−0.356232	−	0.199413i
$43$			10.4587i			1.59494i	0.603357	+	0.797471i	$0.293829\pi$
$43$			10.4587i			1.59494i	−0.603357	+	0.797471i	$0.706171\pi$
$44$	0.490864	−	1.83193i	0.0740006	−	0.276174i
$45$	−0.535417	−	1.99820i	−0.0798152	−	0.297875i
$46$	−2.19807	−	8.20332i	−0.324088	−	1.20951i
$47$	0.482703	−	1.80147i	0.0704095	−	0.262772i	−0.921744	−	0.387799i	$-0.873235\pi$
$47$	0.482703	−	1.80147i	0.0704095	−	0.262772i	0.992153	+	0.125028i	$0.0399020\pi$
$48$			1.00000i			0.144338i
$49$	−5.96712	+	3.65970i	−0.852446	+	0.522815i
$50$	0.509480	−	0.509480i	0.0720513	−	0.0720513i
$51$	2.16164	−	1.24802i	0.302690	−	0.174758i
$52$	3.44034	−	1.07892i	0.477089	−	0.149619i
$53$	2.70278	−	4.68135i	0.371255	−	0.643032i	−0.618504	−	0.785782i	$-0.712261\pi$
$53$	2.70278	−	4.68135i	0.371255	−	0.643032i	0.989759	+	0.142749i	$0.0455942\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$		−	3.92339i		−	0.529029i
$56$	2.30865	+	1.29234i	0.308506	+	0.172696i
$57$	0.522781	+	0.522781i	0.0692440	+	0.0692440i
$58$	2.09771	−	7.82875i	0.275443	−	1.02797i
$59$	12.9998	−	3.48328i	1.69243	−	0.453485i	0.721413	−	0.692505i	$-0.243493\pi$
$59$	12.9998	−	3.48328i	1.69243	−	0.453485i	0.971015	+	0.239021i	$0.0768263\pi$
$60$	0.535417	+	1.99820i	0.0691220	+	0.257967i
$61$	8.23336	−	4.75353i	1.05417	−	0.608628i	0.130359	−	0.991467i	$-0.458387\pi$
$61$	8.23336	−	4.75353i	1.05417	−	0.608628i	0.923815	+	0.382839i	$0.125054\pi$
$62$	−7.48791			−0.950966
$63$	−1.84583	+	1.89550i	−0.232553	+	0.238810i
$64$		−	1.00000i		−	0.125000i
$65$	6.29683	−	3.99791i	0.781025	−	0.495880i
$66$	−1.64246	−	0.948277i	−0.202173	−	0.116725i
$67$	8.60990	−	2.30701i	1.05187	−	0.281847i	0.308843	−	0.951113i	$-0.400058\pi$
$67$	8.60990	−	2.30701i	1.05187	−	0.281847i	0.743023	+	0.669266i	$0.233391\pi$
$68$	−2.16164	+	1.24802i	−0.262138	+	0.151345i
$69$	−8.49270			−1.02240
$70$	5.30509	+	1.34627i	0.634079	+	0.160910i
$71$	−4.51316	−	4.51316i	−0.535614	−	0.535614i	0.386624	−	0.922238i	$-0.373641\pi$
$71$	−4.51316	−	4.51316i	−0.535614	−	0.535614i	−0.922238	+	0.386624i	$0.873641\pi$
$72$	0.965926	+	0.258819i	0.113835	+	0.0305021i
$73$	0.693968	−	0.185948i	0.0812228	−	0.0217636i	−0.217979	−	0.975954i	$-0.569946\pi$
$73$	0.693968	−	0.185948i	0.0812228	−	0.0217636i	0.299202	+	0.954190i	$0.403280\pi$
$74$	−1.53350	+	2.65609i	−0.178265	+	0.308765i
$75$	−0.360257	−	0.623983i	−0.0415989	−	0.0720513i
$76$	−0.522781	−	0.522781i	−0.0599671	−	0.0599671i
$77$	−4.31186	+	2.56637i	−0.491382	+	0.292465i
$78$	−0.151729	−	3.60236i	−0.0171799	−	0.407887i
$79$	4.82081	+	8.34988i	0.542383	+	0.939435i	0.998767	+	0.0496517i	$0.0158111\pi$
$79$	4.82081	+	8.34988i	0.542383	+	0.939435i	−0.456384	+	0.889783i	$0.650856\pi$
$80$	−0.535417	−	1.99820i	−0.0598614	−	0.223406i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.633456	+	1.09718i	0.0699535	+	0.121163i
$83$	1.63597	−	1.63597i	0.179571	−	0.179571i	−0.611598	−	0.791169i	$-0.709473\pi$
$83$	1.63597	−	1.63597i	0.179571	−	0.179571i	0.791169	+	0.611598i	$0.209473\pi$
$84$	1.84583	−	1.89550i	0.201396	−	0.206816i
$85$	−3.65119	+	3.65119i	−0.396027	+	0.396027i
$86$	−10.1024	−	2.70692i	−1.08937	−	0.291895i
$87$	−7.01907	−	4.05246i	−0.752523	−	0.434469i
$88$	1.64246	+	0.948277i	0.175087	+	0.101087i
$89$	−0.868177	+	3.24008i	−0.0920266	+	0.343448i	−0.996552	−	0.0829721i	$-0.973559\pi$
$89$	−0.868177	+	3.24008i	−0.0920266	+	0.343448i	0.904525	+	0.426420i	$0.140225\pi$
$90$	2.06869			0.218059
$91$	−8.51266	−	4.30519i	−0.892369	−	0.451307i
$92$	8.49270			0.885425
$93$	−1.93801	+	7.23277i	−0.200963	+	0.750003i
$94$	1.61516	+	0.932511i	0.166591	+	0.0961812i
$95$	−1.32453	−	0.764717i	−0.135894	−	0.0784583i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	−1.08804	+	1.08804i	−0.110474	+	0.110474i	−0.760183	−	0.649709i	$-0.774891\pi$
$97$	−1.08804	+	1.08804i	−0.110474	+	0.110474i	0.649709	+	0.760183i	$0.274891\pi$
$98$	−1.99060	−	6.71100i	−0.201081	−	0.677913i
$99$	−1.34107	+	1.34107i	−0.134782	+	0.134782i
$100$	0.360257	+	0.623983i	0.0360257	+	0.0623983i
$101$	−2.09697	+	3.63206i	−0.208656	+	0.361403i	−0.951292	−	0.308293i	$-0.900242\pi$
$101$	−2.09697	+	3.63206i	−0.208656	+	0.361403i	0.742635	+	0.669696i	$0.233576\pi$
$102$	0.646025	+	2.41100i	0.0639660	+	0.238724i
$103$	−2.81044	−	4.86783i	−0.276921	−	0.479641i	0.693697	−	0.720267i	$-0.255981\pi$
$103$	−2.81044	−	4.86783i	−0.276921	−	0.479641i	−0.970618	+	0.240626i	$0.922647\pi$
$104$	0.151729	+	3.60236i	0.0148782	+	0.353240i
$105$	2.67346	−	4.77588i	0.260903	−	0.466078i
$106$	3.82230	+	3.82230i	0.371255	+	0.371255i
$107$	−0.379487	−	0.657292i	−0.0366864	−	0.0635428i	0.847099	−	0.531435i	$-0.178347\pi$
$107$	−0.379487	−	0.657292i	−0.0366864	−	0.0635428i	−0.883786	+	0.467892i	$0.845014\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	14.4648	−	3.87584i	1.38548	−	0.371238i	0.512371	−	0.858764i	$-0.328767\pi$
$109$	14.4648	−	3.87584i	1.38548	−	0.371238i	0.873108	+	0.487526i	$0.162101\pi$
$110$	3.78970	+	1.01545i	0.361334	+	0.0968191i
$111$	2.16869	+	2.16869i	0.205843	+	0.205843i
$112$	−1.84583	+	1.89550i	−0.174414	+	0.179108i
$113$	−11.3984			−1.07228			−0.536138	−	0.844131i	$-0.680117\pi$
$113$	−11.3984			−1.07228			−0.536138	+	0.844131i	$0.680117\pi$
$114$	−0.640273	+	0.369662i	−0.0599671	+	0.0346220i
$115$	16.9701	−	4.54714i	1.58247	−	0.424023i
$116$	7.01907	+	4.05246i	0.651704	+	0.376262i
$117$	−3.51888	−	0.785800i	−0.325321	−	0.0726473i
$118$			13.4584i			1.23894i
$119$	6.40103	+	1.62439i	0.586781	+	0.148908i
$120$	−2.06869			−0.188845
$121$	6.41126	−	3.70154i	0.582842	−	0.336504i
$122$	2.46061	+	9.18312i	0.222773	+	0.831401i
$123$	1.22374	−	0.327901i	0.110341	−	0.0295658i
$124$	1.93801	−	7.23277i	0.174039	−	0.649522i
$125$	8.36789	+	8.36789i	0.748447	+	0.748447i
$126$	−1.35318	−	2.27352i	−0.120550	−	0.202542i
$127$			10.4391i			0.926322i	0.886274	+	0.463161i	$0.153285\pi$
$127$			10.4391i			0.926322i	−0.886274	+	0.463161i	$0.846715\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−5.22937	+	9.05753i	−0.460420	+	0.797471i
$130$	2.23195	+	7.11700i	0.195755	+	0.624202i
$131$	16.3242	−	9.42477i	1.42625	−	0.823446i	0.429428	−	0.903101i	$-0.358715\pi$
$131$	16.3242	−	9.42477i	1.42625	−	0.823446i	0.996823	+	0.0796546i	$0.0253817\pi$
$132$	1.34107	−	1.34107i	0.116725	−	0.116725i
$133$	0.0259668	+	1.95589i	0.00225161	+	0.169598i
$134$			8.91362i			0.770020i
$135$	0.535417	−	1.99820i	0.0460813	−	0.171978i
$136$	−0.646025	−	2.41100i	−0.0553962	−	0.206741i
$137$	4.32908	+	16.1564i	0.369858	+	1.38033i	0.860714	+	0.509089i	$0.170018\pi$
$137$	4.32908	+	16.1564i	0.369858	+	1.38033i	−0.490855	+	0.871241i	$0.663316\pi$
$138$	2.19807	−	8.20332i	0.187112	−	0.698313i
$139$		−	16.3078i		−	1.38321i	−0.722276	−	0.691604i	$-0.756904\pi$
$139$		−	16.3078i		−	1.38321i	0.722276	−	0.691604i	$-0.243096\pi$
$140$	−2.67346	+	4.77588i	−0.225948	+	0.403636i
$141$	1.31877	−	1.31877i	0.111060	−	0.111060i
$142$	5.52747	−	3.19129i	0.463855	−	0.267807i
$143$	−6.06062	−	3.16682i	−0.506815	−	0.264823i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	16.1953	+	4.33951i	1.34494	+	0.360377i
$146$			0.718449i			0.0594592i
$147$	−6.99753	+	0.185834i	−0.577147	+	0.0153273i
$148$	−2.16869	−	2.16869i	−0.178265	−	0.178265i
$149$	−2.84914	+	10.6332i	−0.233411	+	0.871102i	0.745448	+	0.666564i	$0.232236\pi$
$149$	−2.84914	+	10.6332i	−0.233411	+	0.871102i	−0.978859	+	0.204538i	$0.934431\pi$
$150$	0.695963	−	0.186483i	0.0568251	−	0.0152262i
$151$	−5.43118	−	20.2695i	−0.441983	−	1.64950i	−0.723780	−	0.690031i	$-0.757597\pi$
$151$	−5.43118	−	20.2695i	−0.441983	−	1.64950i	0.281797	−	0.959474i	$-0.409070\pi$
$152$	0.640273	−	0.369662i	0.0519330	−	0.0299835i
$153$	2.49605			0.201794
$154$	−1.36293	−	4.82917i	−0.109828	−	0.389145i
$155$		−	15.4902i		−	1.24420i
$156$	3.51888	+	0.785800i	0.281736	+	0.0629144i
$157$	12.5512	+	7.24646i	1.00170	+	0.578331i	0.908750	−	0.417340i	$-0.137038\pi$
$157$	12.5512	+	7.24646i	1.00170	+	0.578331i	0.0929479	+	0.995671i	$0.470371\pi$
$158$	−9.31308	+	2.49543i	−0.740909	+	0.198526i
$159$	4.68135	−	2.70278i	0.371255	−	0.214344i
$160$	2.06869			0.163544
$161$	−16.0979	−	15.6761i	−1.26869	−	1.23545i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−16.1817	−	4.33588i	−1.26745	−	0.339612i	−0.438396	−	0.898782i	$-0.644453\pi$
$163$	−16.1817	−	4.33588i	−1.26745	−	0.339612i	−0.829053	+	0.559170i	$0.811120\pi$
$164$	−1.22374	+	0.327901i	−0.0955583	+	0.0256048i
$165$	1.96169	−	3.39775i	0.152718	−	0.264515i
$166$	1.15681	+	2.00365i	0.0897857	+	0.155513i
$167$	12.6275	+	12.6275i	0.977145	+	0.977145i	0.999745	−	0.0225997i	$-0.00719433\pi$
$167$	12.6275	+	12.6275i	0.977145	+	0.977145i	−0.0225997	+	0.999745i	$0.507194\pi$
$168$	1.35318	+	2.27352i	0.104400	+	0.175406i
$169$	−1.09316	−	12.9540i	−0.0840893	−	0.996458i
$170$	−2.58178	−	4.47177i	−0.198013	−	0.342969i
$171$	0.191351	+	0.714132i	0.0146330	+	0.0546110i
$172$	5.22937	−	9.05753i	0.398736	−	0.690630i
$173$	2.45036	+	4.24415i	0.186297	+	0.322677i	0.944013	−	0.329908i	$-0.107018\pi$
$173$	2.45036	+	4.24415i	0.186297	+	0.322677i	−0.757716	+	0.652585i	$0.773685\pi$
$174$	5.73105	−	5.73105i	0.434469	−	0.434469i
$175$	0.468899	−	1.84773i	0.0354455	−	0.139675i
$176$	−1.34107	+	1.34107i	−0.101087	+	0.101087i
$177$	12.9998	+	3.48328i	0.977123	+	0.261819i
$178$	−2.90498	−	1.67719i	−0.217737	−	0.125711i
$179$	7.09276	+	4.09501i	0.530138	+	0.306075i	0.741073	−	0.671425i	$-0.234317\pi$
$179$	7.09276	+	4.09501i	0.530138	+	0.306075i	−0.210935	+	0.977500i	$0.567651\pi$
$180$	−0.535417	+	1.99820i	−0.0399076	+	0.148937i
$181$	−4.96102			−0.368750			−0.184375	−	0.982856i	$-0.559026\pi$
$181$	−4.96102			−0.368750			−0.184375	+	0.982856i	$0.559026\pi$
$182$	6.36173	−	7.10833i	0.471563	−	0.526904i
$183$	9.50707			0.702783
$184$	−2.19807	+	8.20332i	−0.162044	+	0.604757i
$185$	−5.49464	−	3.17233i	−0.403974	−	0.233234i
$186$	−6.48472	−	3.74396i	−0.475483	−	0.274520i
$187$	4.57259	+	1.22522i	0.334381	+	0.0895971i
$188$	−1.31877	+	1.31877i	−0.0961812	+	0.0961812i
$189$	−2.54628	+	0.718636i	−0.185215	+	0.0522731i
$190$	1.08147	−	1.08147i	0.0784583	−	0.0784583i
$191$	5.98826	+	10.3720i	0.433295	+	0.750489i	0.997155	−	0.0753815i	$-0.0240175\pi$
$191$	5.98826	+	10.3720i	0.433295	+	0.750489i	−0.563860	+	0.825871i	$0.690684\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	3.43795	+	12.8306i	0.247469	+	0.923568i	0.972126	+	0.234458i	$0.0753316\pi$
$193$	3.43795	+	12.8306i	0.247469	+	0.923568i	−0.724657	+	0.689110i	$0.758002\pi$
$194$	−0.769362	−	1.33257i	−0.0552369	−	0.0956732i
$195$	7.45217	−	0.313880i	0.533661	−	0.0224774i
$196$	6.99753	−	0.185834i	0.499824	−	0.0132738i
$197$	−7.34311	−	7.34311i	−0.523175	−	0.523175i	0.395354	−	0.918529i	$-0.370622\pi$
$197$	−7.34311	−	7.34311i	−0.523175	−	0.523175i	−0.918529	+	0.395354i	$0.870622\pi$
$198$	−0.948277	−	1.64246i	−0.0673911	−	0.116725i
$199$	−0.781653	+	1.35386i	−0.0554099	+	0.0959727i	−0.892400	−	0.451245i	$-0.850980\pi$
$199$	−0.781653	+	1.35386i	−0.0554099	+	0.0959727i	0.836990	+	0.547218i	$0.184313\pi$
$200$	−0.695963	+	0.186483i	−0.0492120	+	0.0131863i
$201$	8.60990	+	2.30701i	0.607295	+	0.162724i
$202$	−2.96556	−	2.96556i	−0.208656	−	0.208656i
$203$	−5.82449	−	20.6374i	−0.408799	−	1.44846i
$204$	−2.49605			−0.174758
$205$	−2.26972	+	1.31043i	−0.158524	+	0.0915241i
$206$	5.42935	−	1.45479i	0.378281	−	0.101360i
$207$	−7.35489	−	4.24635i	−0.511200	−	0.295142i
$208$	−3.51888	−	0.785800i	−0.243990	−	0.0544854i
$209$			1.40217i			0.0969900i
$210$	3.92120	+	3.81845i	0.270589	+	0.263498i
$211$	−27.0456			−1.86190			−0.930948	−	0.365153i	$-0.881017\pi$
$211$	−27.0456			−1.86190			−0.930948	+	0.365153i	$0.881017\pi$
$212$	−4.68135	+	2.70278i	−0.321516	+	0.185627i
$213$	−1.65193	−	6.16510i	−0.113189	−	0.422426i
$214$	0.733114	−	0.196437i	0.0501146	−	0.0134282i
$215$	5.59979	−	20.8987i	0.381902	−	1.42528i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−17.0240	+	10.1325i	−1.15566	+	0.687837i
$218$			14.9751i			1.01424i
$219$	0.693968	+	0.185948i	0.0468940	+	0.0125652i
$220$	−1.96169	+	3.39775i	−0.132257	+	0.229076i
$221$	2.69303	+	8.58726i	0.181153	+	0.577641i
$222$	−2.65609	+	1.53350i	−0.178265	+	0.102922i
$223$	−12.4943	+	12.4943i	−0.836678	+	0.836678i	−0.988420	−	0.151742i	$-0.951512\pi$
$223$	−12.4943	+	12.4943i	−0.836678	+	0.836678i	0.151742	+	0.988420i	$0.451512\pi$
$224$	−1.35318	−	2.27352i	−0.0904129	−	0.151906i
$225$		−	0.720513i		−	0.0480342i
$226$	2.95013	−	11.0101i	0.196240	−	0.732378i
$227$	−4.90540	−	18.3072i	−0.325583	−	1.21509i	−0.913725	−	0.406334i	$-0.866807\pi$
$227$	−4.90540	−	18.3072i	−0.325583	−	1.21509i	0.588142	−	0.808758i	$-0.299860\pi$
$228$	−0.191351	−	0.714132i	−0.0126725	−	0.0472945i
$229$	−2.21022	+	8.24865i	−0.146055	+	0.545086i	0.853651	+	0.520846i	$0.174383\pi$
$229$	−2.21022	+	8.24865i	−0.146055	+	0.545086i	−0.999706	+	0.0242405i	$0.992283\pi$
$230$			17.5688i			1.15845i
$231$	−5.01737	+	0.0666115i	−0.330119	+	0.00438271i
$232$	−5.73105	+	5.73105i	−0.376262	+	0.376262i
$233$	−11.1360	+	6.42938i	−0.729544	+	0.421202i	−0.818255	−	0.574855i	$-0.805058\pi$
$233$	−11.1360	+	6.42938i	−0.729544	+	0.421202i	0.0887114	+	0.996057i	$0.471725\pi$
$234$	1.66978	−	3.19560i	0.109157	−	0.208903i
$235$	−1.92908	+	3.34126i	−0.125839	+	0.217960i
$236$	−12.9998	−	3.48328i	−0.846214	−	0.226742i
$237$			9.64161i			0.626290i
$238$	−3.22575	+	5.76250i	−0.209094	+	0.373527i
$239$	11.1656	+	11.1656i	0.722246	+	0.722246i	0.969062	−	0.246817i	$-0.0793846\pi$
$239$	11.1656	+	11.1656i	0.722246	+	0.722246i	−0.246817	+	0.969062i	$0.579385\pi$
$240$	0.535417	−	1.99820i	0.0345610	−	0.128983i
$241$	3.08971	−	0.827886i	0.199026	−	0.0533289i	−0.157929	−	0.987450i	$-0.550482\pi$
$241$	3.08971	−	0.827886i	0.199026	−	0.0533289i	0.356955	+	0.934122i	$0.383815\pi$
$242$	1.91606	+	7.15083i	0.123169	+	0.459673i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−9.50707			−0.608628
$245$	13.8830	−	4.11793i	0.886952	−	0.263085i
$246$			1.26691i			0.0807754i
$247$	−2.25040	+	1.42880i	−0.143190	+	0.0909125i
$248$	6.48472	+	3.74396i	0.411780	+	0.237742i
$249$	2.23478	−	0.598808i	0.141624	−	0.0379479i
$250$	−10.2485	+	5.91699i	−0.648174	+	0.374223i
$251$	11.0842			0.699628			0.349814	−	0.936819i	$-0.386245\pi$
$251$	11.0842			0.699628			0.349814	+	0.936819i	$0.386245\pi$
$252$	2.54628	−	0.718636i	0.160401	−	0.0452698i
$253$	−11.3893	−	11.3893i	−0.716038	−	0.716038i
$254$	−10.0834	−	2.70184i	−0.632690	−	0.169529i
$255$	−4.98761	+	1.33643i	−0.312336	+	0.0836903i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.23585	−	5.60466i	−0.201847	−	0.349609i	0.747277	−	0.664513i	$-0.231361\pi$
$257$	−3.23585	−	5.60466i	−0.201847	−	0.349609i	−0.949124	+	0.314904i	$0.898028\pi$
$258$	−7.39544	−	7.39544i	−0.460420	−	0.460420i
$259$	0.107720	+	8.11378i	0.00669340	+	0.504166i
$260$	−7.45217	+	0.313880i	−0.462164	+	0.0194660i
$261$	−4.05246	−	7.01907i	−0.250841	−	0.434469i
$262$	4.87862	+	18.2073i	0.301402	+	1.12485i
$263$	−1.88597	+	3.26660i	−0.116294	+	0.201427i	−0.918296	−	0.395894i	$-0.870435\pi$
$263$	−1.88597	+	3.26660i	−0.116294	+	0.201427i	0.802002	+	0.597321i	$0.203768\pi$
$264$	0.948277	+	1.64246i	0.0583624	+	0.101087i
$265$	−7.90717	+	7.90717i	−0.485734	+	0.485734i
$266$	−1.89597	−	0.481141i	−0.116249	−	0.0295006i
$267$	−2.37190	+	2.37190i	−0.145158	+	0.145158i
$268$	−8.60990	−	2.30701i	−0.525933	−	0.140923i
$269$	−17.0994	−	9.87236i	−1.04257	−	0.601929i	−0.122011	−	0.992529i	$-0.538934\pi$
$269$	−17.0994	−	9.87236i	−1.04257	−	0.601929i	−0.920560	+	0.390600i	$0.872268\pi$
$270$	1.79154	+	1.03435i	0.109030	+	0.0629483i
$271$	5.29606	−	19.7652i	0.321713	−	1.20065i	−0.595863	−	0.803086i	$-0.703190\pi$
$271$	5.29606	−	19.7652i	0.321713	−	1.20065i	0.917575	−	0.397562i	$-0.130144\pi$
$272$	2.49605			0.151345
$273$	−5.21958	−	7.98473i	−0.315903	−	0.483258i
$274$	−16.7263			−1.01047
$275$	0.353674	−	1.31993i	0.0213274	−	0.0795948i
$276$	7.35489	+	4.24635i	0.442713	+	0.255600i
$277$	−9.03468	−	5.21618i	−0.542841	−	0.313410i	0.203388	−	0.979098i	$-0.434805\pi$
$277$	−9.03468	−	5.21618i	−0.542841	−	0.313410i	−0.746230	+	0.665689i	$0.768138\pi$
$278$	15.7521	+	4.22077i	0.944749	+	0.253145i
$279$	−5.29475	+	5.29475i	−0.316989	+	0.316989i
$280$	−3.92120	−	3.81845i	−0.234337	−	0.228196i
$281$	−11.6966	+	11.6966i	−0.697760	+	0.697760i	−0.963927	−	0.266167i	$-0.914243\pi$
$281$	−11.6966	+	11.6966i	−0.697760	+	0.697760i	0.266167	+	0.963927i	$0.414243\pi$
$282$	0.932511	+	1.61516i	0.0555302	+	0.0961812i
$283$	9.94003	−	17.2166i	0.590874	−	1.02342i	−0.403242	−	0.915094i	$-0.632117\pi$
$283$	9.94003	−	17.2166i	0.590874	−	1.02342i	0.994115	−	0.108329i	$-0.0345501\pi$
$284$	1.65193	+	6.16510i	0.0980242	+	0.365831i
$285$	−0.764717	−	1.32453i	−0.0452979	−	0.0784583i
$286$	4.62752	−	5.03448i	0.273631	−	0.297695i
$287$	2.92485	+	1.63728i	0.172649	+	0.0966458i
$288$	−0.707107	−	0.707107i	−0.0416667	−	0.0416667i
$289$	5.38487	+	9.32687i	0.316757	+	0.548639i
$290$	−8.38329	+	14.5203i	−0.492284	+	0.852661i
$291$	−1.48629	+	0.398251i	−0.0871280	+	0.0233459i
$292$	−0.693968	−	0.185948i	−0.0406114	−	0.0108818i
$293$	9.58678	+	9.58678i	0.560065	+	0.560065i	0.929326	−	0.369261i	$-0.120389\pi$
$293$	9.58678	+	9.58678i	0.560065	+	0.560065i	−0.369261	+	0.929326i	$0.620389\pi$
$294$	1.63159	−	6.80719i	0.0951564	−	0.397004i
$295$	−27.8412			−1.62098
$296$	2.65609	−	1.53350i	0.154382	−	0.0891327i
$297$	−1.83193	+	0.490864i	−0.106299	+	0.0284828i
$298$	−9.53342	−	5.50412i	−0.552256	−	0.318845i
$299$	6.67357	−	29.8848i	0.385942	−	1.72828i
$300$			0.720513i			0.0415989i
$301$	−26.6309	+	7.51603i	−1.53498	+	0.433217i
$302$	20.9845			1.20752
$303$	−3.63206	+	2.09697i	−0.208656	+	0.120468i
$304$	0.191351	+	0.714132i	0.0109747	+	0.0409583i
$305$	−18.9971	+	5.09024i	−1.08777	+	0.291467i
$306$	−0.646025	+	2.41100i	−0.0369308	+	0.137828i
$307$	21.4796	+	21.4796i	1.22590	+	1.22590i	0.965500	+	0.260405i	$0.0838560\pi$
$307$	21.4796	+	21.4796i	1.22590	+	1.22590i	0.260405	+	0.965500i	$0.416144\pi$
$308$	5.01737	−	0.0666115i	0.285891	−	0.00379554i
$309$		−	5.62088i		−	0.319761i
$310$	14.9624	+	4.00916i	0.849806	+	0.227705i
$311$	−0.270874	+	0.469167i	−0.0153599	+	0.0266040i	−0.873603	−	0.486639i	$-0.838223\pi$
$311$	−0.270874	+	0.469167i	−0.0153599	+	0.0266040i	0.858243	+	0.513243i	$0.171556\pi$
$312$	−1.66978	+	3.19560i	−0.0945326	+	0.180915i
$313$	−13.5790	+	7.83985i	−0.767531	+	0.443135i	−0.831993	−	0.554786i	$-0.812800\pi$
$313$	−13.5790	+	7.83985i	−0.767531	+	0.443135i	0.0644618	+	0.997920i	$0.479467\pi$
$314$	−10.2480	+	10.2480i	−0.578331	+	0.578331i
$315$	4.70322	−	2.79930i	0.264997	−	0.157723i
$316$		−	9.64161i		−	0.542383i
$317$	−0.296338	+	1.10595i	−0.0166440	+	0.0621163i	−0.973748	−	0.227627i	$-0.926903\pi$
$317$	−0.296338	+	1.10595i	−0.0166440	+	0.0621163i	0.957104	+	0.289743i	$0.0935700\pi$
$318$	1.39906	+	5.22136i	0.0784554	+	0.292800i
$319$	−3.97842	−	14.8477i	−0.222749	−	0.831309i
$320$	−0.535417	+	1.99820i	−0.0299307	+	0.111703i
$321$		−	0.758975i		−	0.0423619i
$322$	19.3084	−	11.4921i	1.07601	−	0.640431i
$323$	1.30489	−	1.30489i	0.0726058	−	0.0726058i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	2.47881	−	0.777374i	0.137500	−	0.0431210i
$326$	8.37627	−	14.5081i	0.463919	−	0.803531i
$327$	14.4648	+	3.87584i	0.799907	+	0.214334i
$328$		−	1.26691i		−	0.0699535i
$329$	4.93395	−	0.0655040i	0.272017	−	0.00361135i
$330$	2.77425	+	2.77425i	0.152718	+	0.152718i
$331$	4.14933	−	15.4855i	0.228068	−	0.851161i	−0.753084	−	0.657924i	$-0.771435\pi$
$331$	4.14933	−	15.4855i	0.228068	−	0.851161i	0.981152	−	0.193237i	$-0.0618986\pi$
$332$	−2.23478	+	0.598808i	−0.122650	+	0.0328639i
$333$	0.793796	+	2.96249i	0.0434998	+	0.162343i
$334$	−15.4655	+	8.92899i	−0.846232	+	0.488572i
$335$	−18.4395			−1.00746
$336$	−2.54628	+	0.718636i	−0.138911	+	0.0392048i
$337$		−	10.4788i		−	0.570818i	−0.958406	−	0.285409i	$-0.907871\pi$
$337$		−	10.4788i		−	0.570818i	0.958406	−	0.285409i	$-0.0921295\pi$
$338$	12.7955	+	2.29682i	0.695983	+	0.124930i
$339$	−9.87134	−	5.69922i	−0.536138	−	0.309539i
$340$	4.98761	−	1.33643i	0.270491	−	0.0724779i
$341$	−12.2986	+	7.10062i	−0.666008	+	0.384520i
$342$	−0.739324			−0.0399780
$343$	−13.6068	−	12.5640i	−0.734700	−	0.678392i
$344$	7.39544	+	7.39544i	0.398736	+	0.398736i
$345$	16.9701	+	4.54714i	0.913642	+	0.244810i
$346$	−4.73373	+	1.26840i	−0.254487	+	0.0681896i
$347$	11.9993	−	20.7834i	0.644158	−	1.11571i	−0.340338	−	0.940303i	$-0.610541\pi$
$347$	11.9993	−	20.7834i	0.644158	−	1.11571i	0.984495	−	0.175411i	$-0.0561253\pi$
$348$	4.05246	+	7.01907i	0.217235	+	0.376262i
$349$	−6.10083	−	6.10083i	−0.326570	−	0.326570i	0.524711	−	0.851281i	$-0.324174\pi$
$349$	−6.10083	−	6.10083i	−0.326570	−	0.326570i	−0.851281	+	0.524711i	$0.824174\pi$
$350$	1.66341	+	0.931150i	0.0889131	+	0.0497721i
$351$	−2.65454	−	2.43996i	−0.141689	−	0.130236i
$352$	−0.948277	−	1.64246i	−0.0505433	−	0.0875436i
$353$	8.75886	+	32.6885i	0.466187	+	1.73983i	0.652924	+	0.757424i	$0.273542\pi$
$353$	8.75886	+	32.6885i	0.466187	+	1.73983i	−0.186737	+	0.982410i	$0.559791\pi$
$354$	−6.72918	+	11.6553i	−0.357652	+	0.619471i
$355$	6.60179	+	11.4346i	0.350387	+	0.606888i
$356$	2.37190	−	2.37190i	0.125711	−	0.125711i
$357$	4.73126	+	4.60728i	0.250405	+	0.243843i
$358$	−5.79122	+	5.79122i	−0.306075	+	0.306075i
$359$	−31.0381	−	8.31664i	−1.63813	−	0.438935i	−0.681874	−	0.731470i	$-0.738835\pi$
$359$	−31.0381	−	8.31664i	−1.63813	−	0.438935i	−0.956255	+	0.292534i	$0.905501\pi$
$360$	−1.79154	−	1.03435i	−0.0944224	−	0.0545148i
$361$	−15.9811	−	9.22670i	−0.841111	−	0.485616i
$362$	1.28401	−	4.79198i	0.0674859	−	0.251861i
$363$	7.40308			0.388561
$364$	5.21958	+	7.98473i	0.273580	+	0.418514i
$365$	−1.48625			−0.0777938
$366$	−2.46061	+	9.18312i	−0.128618	+	0.480010i
$367$	11.7708	+	6.79586i	0.614429	+	0.354741i	0.774697	−	0.632333i	$-0.217902\pi$
$367$	11.7708	+	6.79586i	0.614429	+	0.354741i	−0.160268	+	0.987074i	$0.551236\pi$
$368$	−7.35489	−	4.24635i	−0.383400	−	0.221356i
$369$	1.22374	+	0.327901i	0.0637055	+	0.0170698i
$370$	4.48635	−	4.48635i	0.233234	−	0.233234i
$371$	13.8624	+	3.51785i	0.719697	+	0.182638i
$372$	5.29475	−	5.29475i	0.274520	−	0.274520i
$373$	−14.0828	−	24.3922i	−0.729181	−	1.26298i	−0.957230	−	0.289329i	$-0.906568\pi$
$373$	−14.0828	−	24.3922i	−0.729181	−	1.26298i	0.228048	−	0.973650i	$-0.426766\pi$
$374$	−2.36695	+	4.09967i	−0.122392	+	0.211989i
$375$	3.06286	+	11.4307i	0.158165	+	0.590281i
$376$	−0.932511	−	1.61516i	−0.0480906	−	0.0832953i
$377$	19.7757	−	21.5148i	1.01850	−	1.10807i
$378$	−0.0351224	−	2.64552i	−0.00180650	−	0.136071i
$379$	6.88941	+	6.88941i	0.353885	+	0.353885i	0.861553	−	0.507668i	$-0.169492\pi$
$379$	6.88941	+	6.88941i	0.353885	+	0.353885i	−0.507668	+	0.861553i	$0.669492\pi$
$380$	0.764717	+	1.32453i	0.0392291	+	0.0679468i
$381$	−5.21956	+	9.04054i	−0.267406	+	0.463161i
$382$	−11.5684	+	3.09975i	−0.591892	+	0.158597i
$383$	16.8628	+	4.51837i	0.861649	+	0.230878i	0.662473	−	0.749086i	$-0.269507\pi$
$383$	16.8628	+	4.51837i	0.861649	+	0.230878i	0.199176	+	0.979964i	$0.436174\pi$
$384$	0.707107	+	0.707107i	0.0360844	+	0.0360844i
$385$	9.99006	−	2.81949i	0.509140	−	0.143694i
$386$	−13.2832			−0.676099
$387$	−9.05753	+	5.22937i	−0.460420	+	0.265824i
$388$	1.48629	−	0.398251i	0.0754551	−	0.0202181i
$389$	−12.2815	−	7.09075i	−0.622699	−	0.359515i	0.155220	−	0.987880i	$-0.450391\pi$
$389$	−12.2815	−	7.09075i	−0.622699	−	0.359515i	−0.777919	+	0.628365i	$0.783725\pi$
$390$	−1.62558	+	7.27948i	−0.0823144	+	0.368611i
$391$			21.1982i			1.07204i
$392$	−1.63159	+	6.80719i	−0.0824079	+	0.343815i
$393$	18.8495			0.950834
$394$	8.99344	−	5.19236i	0.453083	−	0.261587i
$395$	−5.16228	−	19.2659i	−0.259743	−	0.969372i
$396$	1.83193	−	0.490864i	0.0920580	−	0.0246669i
$397$	−3.64533	+	13.6046i	−0.182954	+	0.682793i	0.812105	+	0.583511i	$0.198321\pi$
$397$	−3.64533	+	13.6046i	−0.182954	+	0.682793i	−0.995059	+	0.0992823i	$0.968345\pi$
$398$	−1.10542	−	1.10542i	−0.0554099	−	0.0554099i
$399$	−0.955459	+	1.70684i	−0.0478328	+	0.0854488i
$400$		−	0.720513i		−	0.0360257i
$401$	26.0592	+	6.98254i	1.30133	+	0.348692i	0.841955	−	0.539548i	$-0.181405\pi$
$401$	26.0592	+	6.98254i	1.30133	+	0.348692i	0.459380	+	0.888240i	$0.348072\pi$
$402$	−4.45681	+	7.71942i	−0.222285	+	0.385010i
$403$	−23.9284	−	12.5032i	−1.19196	−	0.622826i
$404$	3.63206	−	2.09697i	0.180702	−	0.104328i
$405$	1.46279	−	1.46279i	0.0726864	−	0.0726864i
$406$	21.4417	−	0.284664i	1.06413	−	0.0141276i
$407$			5.81672i			0.288324i
$408$	0.646025	−	2.41100i	0.0319830	−	0.119362i
$409$	−6.46638	−	24.1329i	−0.319742	−	1.19329i	−0.919493	−	0.393106i	$-0.871400\pi$
$409$	−6.46638	−	24.1329i	−0.319742	−	1.19329i	0.599751	−	0.800187i	$-0.295266\pi$
$410$	−0.678326	−	2.53155i	−0.0335001	−	0.125024i
$411$	−4.32908	+	16.1564i	−0.213538	+	0.796934i
$412$			5.62088i			0.276921i
$413$	18.2115	+	30.5979i	0.896131	+	1.50563i
$414$	6.00525	−	6.00525i	0.295142	−	0.295142i
$415$	−4.14494	+	2.39308i	−0.203467	+	0.117472i
$416$	1.66978	−	3.19560i	0.0818676	−	0.156677i
$417$	8.15390	−	14.1230i	0.399298	−	0.691604i
$418$	−1.35439	−	0.362908i	−0.0662454	−	0.0177504i
$419$		−	4.75756i		−	0.232422i	−0.993225	−	0.116211i	$-0.962925\pi$
$419$		−	4.75756i		−	0.232422i	0.993225	−	0.116211i	$-0.0370749\pi$
$420$	−4.70322	+	2.79930i	−0.229494	+	0.136592i
$421$	8.93076	+	8.93076i	0.435258	+	0.435258i	0.890413	−	0.455154i	$-0.150416\pi$
$421$	8.93076	+	8.93076i	0.435258	+	0.435258i	−0.455154	+	0.890413i	$0.650416\pi$
$422$	6.99991	−	26.1240i	0.340751	−	1.27170i
$423$	1.80147	−	0.482703i	0.0875906	−	0.0234698i
$424$	−1.39906	−	5.22136i	−0.0679444	−	0.253572i
$425$	−1.55749	+	0.899218i	−0.0755495	+	0.0436185i
$426$	6.38258			0.309237
$427$	18.0206	+	17.5484i	0.872080	+	0.849227i
$428$			0.758975i			0.0366864i
$429$	−3.66524	−	5.77286i	−0.176960	−	0.278716i
$430$	18.7372	+	10.8180i	0.903590	+	0.521688i
$431$	5.81472	−	1.55805i	0.280085	−	0.0750485i	−0.116042	−	0.993244i	$-0.537021\pi$
$431$	5.81472	−	1.55805i	0.280085	−	0.0750485i	0.396127	+	0.918196i	$0.370354\pi$
$432$	−0.866025	+	0.500000i	−0.0416667	+	0.0240563i
$433$	28.5687			1.37292			0.686462	−	0.727166i	$-0.259163\pi$
$433$	28.5687			1.37292			0.686462	+	0.727166i	$0.259163\pi$
$434$	−5.38109	−	19.0664i	−0.258300	−	0.915214i
$435$	11.8558	+	11.8558i	0.568441	+	0.568441i
$436$	−14.4648	−	3.87584i	−0.692740	−	0.185619i
$437$	−6.06491	+	1.62509i	−0.290124	+	0.0777385i
$438$	−0.359224	+	0.622195i	−0.0171644	+	0.0297296i
$439$	1.21420	+	2.10306i	0.0579508	+	0.100374i	0.893545	−	0.448973i	$-0.148210\pi$
$439$	1.21420	+	2.10306i	0.0579508	+	0.100374i	−0.835595	+	0.549347i	$0.814877\pi$
$440$	−2.77425	−	2.77425i	−0.132257	−	0.132257i
$441$	−6.15296	−	3.33783i	−0.292998	−	0.158944i
$442$	−8.99166	+	0.378722i	−0.427690	+	0.0180140i
$443$	10.2364	+	17.7300i	0.486347	+	0.842377i	0.999877	−	0.0156943i	$-0.00499587\pi$
$443$	10.2364	+	17.7300i	0.486347	+	0.842377i	−0.513530	+	0.858072i	$0.671663\pi$
$444$	−0.793796	−	2.96249i	−0.0376719	−	0.140593i
$445$	3.46959	−	6.00950i	0.164474	−	0.284878i
$446$	−8.83478	−	15.3023i	−0.418339	−	0.724585i
$447$	−7.78401	+	7.78401i	−0.368171	+	0.368171i
$448$	2.54628	−	0.718636i	0.120301	−	0.0339524i
$449$	23.9396	−	23.9396i	1.12978	−	1.12978i	0.139567	−	0.990213i	$-0.455429\pi$
$449$	23.9396	−	23.9396i	1.12978	−	1.12978i	0.990213	−	0.139567i	$-0.0445712\pi$
$450$	0.695963	+	0.186483i	0.0328080	+	0.00879087i
$451$	2.08086	+	1.20138i	0.0979838	+	0.0565710i
$452$	9.87134	+	5.69922i	0.464309	+	0.268069i
$453$	5.43118	−	20.2695i	0.255179	−	0.952342i
$454$	18.9530			0.889509
$455$	14.7049	+	13.1605i	0.689378	+	0.616972i
$456$	0.739324			0.0346220
$457$	−4.92051	+	18.3636i	−0.230172	+	0.859013i	0.750094	+	0.661331i	$0.230008\pi$
$457$	−4.92051	+	18.3636i	−0.230172	+	0.859013i	−0.980266	+	0.197682i	$0.936659\pi$
$458$	−7.39554	−	4.26982i	−0.345571	−	0.199515i
$459$	2.16164	+	1.24802i	0.100897	+	0.0582528i
$460$	−16.9701	−	4.54714i	−0.791237	−	0.212011i
$461$	−2.30429	+	2.30429i	−0.107321	+	0.107321i	−0.758728	−	0.651407i	$-0.774179\pi$
$461$	−2.30429	+	2.30429i	−0.107321	+	0.107321i	0.651407	+	0.758728i	$0.274179\pi$
$462$	1.23425	−	4.86365i	0.0574225	−	0.226277i
$463$	−10.7497	+	10.7497i	−0.499583	+	0.499583i	−0.911308	−	0.411725i	$-0.864926\pi$
$463$	−10.7497	+	10.7497i	−0.499583	+	0.499583i	0.411725	+	0.911308i	$0.364926\pi$
$464$	−4.05246	−	7.01907i	−0.188131	−	0.325852i
$465$	7.74509	−	13.4149i	0.359170	−	0.622101i
$466$	−3.32809	−	12.4206i	−0.154171	−	0.575373i
$467$	3.84255	+	6.65549i	0.177812	+	0.307979i	0.941131	−	0.338043i	$-0.109765\pi$
$467$	3.84255	+	6.65549i	0.177812	+	0.307979i	−0.763319	+	0.646022i	$0.776431\pi$
$468$	2.65454	+	2.43996i	0.122706	+	0.112787i
$469$	12.0617	+	20.2653i	0.556957	+	0.935766i
$470$	−2.72813	−	2.72813i	−0.125839	−	0.125839i
$471$	7.24646	+	12.5512i	0.333899	+	0.578331i
$472$	6.72918	−	11.6553i	0.309736	−	0.536478i
$473$	−19.1597	+	5.13382i	−0.880963	+	0.236053i
$474$	−9.31308	−	2.49543i	−0.427764	−	0.114619i
$475$	−0.376671	−	0.376671i	−0.0172828	−	0.0172828i
$476$	−4.73126	−	4.60728i	−0.216857	−	0.211174i
$477$	5.40555			0.247503
$478$	−13.6751	+	7.89530i	−0.625483	+	0.361123i
$479$	−19.0987	+	5.11748i	−0.872642	+	0.233824i	−0.667230	−	0.744852i	$-0.732520\pi$
$479$	−19.0987	+	5.11748i	−0.872642	+	0.233824i	−0.205412	+	0.978676i	$0.565853\pi$
$480$	1.79154	+	1.03435i	0.0817722	+	0.0472112i
$481$	−9.33552	+	5.92721i	−0.425663	+	0.270257i
$482$			3.19871i			0.145697i
$483$	−6.10316	−	21.6248i	−0.277703	−	0.983964i
$484$	−7.40308			−0.336504
$485$	2.75668	−	1.59157i	0.125175	−	0.0722696i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	24.9150	−	6.67597i	1.12901	−	0.302517i	0.354485	−	0.935062i	$-0.384656\pi$
$487$	24.9150	−	6.67597i	1.12901	−	0.302517i	0.774524	+	0.632545i	$0.217990\pi$
$488$	2.46061	−	9.18312i	0.111387	−	0.415700i
$489$	−11.8458	−	11.8458i	−0.535687	−	0.535687i
$490$	0.384433	+	14.4757i	0.0173669	+	0.653947i
$491$			31.8912i			1.43923i	0.694372	+	0.719616i	$0.255682\pi$
$491$			31.8912i			1.43923i	−0.694372	+	0.719616i	$0.744318\pi$
$492$	−1.22374	−	0.327901i	−0.0551706	−	0.0147829i
$493$	−10.1151	+	17.5199i	−0.455563	+	0.789058i
$494$	−0.797669	−	2.54352i	−0.0358888	−	0.114439i
$495$	3.39775	−	1.96169i	0.152718	−	0.0881716i
$496$	−5.29475	+	5.29475i	−0.237742	+	0.237742i
$497$	8.24848	−	14.7351i	0.369995	−	0.660961i
$498$			2.31362i			0.103676i
$499$	−3.51862	+	13.1317i	−0.157515	+	0.587854i	0.841362	+	0.540472i	$0.181754\pi$
$499$	−3.51862	+	13.1317i	−0.157515	+	0.587854i	−0.998877	+	0.0473819i	$0.984912\pi$
$500$	−3.06286	−	11.4307i	−0.136975	−	0.511199i
$501$	4.62198	+	17.2495i	0.206495	+	0.770650i
$502$	−2.86880	+	10.7065i	−0.128041	+	0.477855i
$503$		−	43.5652i		−	1.94248i	−0.238106	−	0.971239i	$-0.576527\pi$
$503$		−	43.5652i		−	1.94248i	0.238106	−	0.971239i	$-0.423473\pi$
$504$	0.0351224	+	2.64552i	0.00156447	+	0.117841i
$505$	6.13484	−	6.13484i	0.272997	−	0.272997i
$506$	13.9490	−	8.05343i	0.620107	−	0.358019i
$507$	5.53027	−	11.7650i	0.245608	−	0.522504i
$508$	5.21956	−	9.04054i	0.231580	−	0.401109i
$509$	34.5238	+	9.25062i	1.53024	+	0.410026i	0.923097	−	0.384567i	$-0.125649\pi$
$509$	34.5238	+	9.25062i	1.53024	+	0.410026i	0.607142	+	0.794593i	$0.292316\pi$
$510$		−	5.16356i		−	0.228646i
$511$	0.972188	+	1.63341i	0.0430070	+	0.0722579i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.191351	+	0.714132i	−0.00844836	+	0.0315297i
$514$	6.25118	−	1.67500i	0.275728	−	0.0738811i
$515$	3.00951	+	11.2317i	0.132615	+	0.494926i
$516$	9.05753	−	5.22937i	0.398736	−	0.230210i
$517$	3.53712			0.155562
$518$	−7.86519	−	1.99595i	−0.345577	−	0.0876971i
$519$			4.90072i			0.215118i
$520$	1.62558	−	7.27948i	0.0712863	−	0.319226i
$521$	−23.9727	−	13.8407i	−1.05026	−	0.606371i	−0.127541	−	0.991833i	$-0.540709\pi$
$521$	−23.9727	−	13.8407i	−1.05026	−	0.606371i	−0.922723	+	0.385463i	$0.874042\pi$
$522$	7.82875	−	2.09771i	0.342655	−	0.0918142i
$523$	−3.26644	+	1.88588i	−0.142831	+	0.0824638i	−0.569713	−	0.821844i	$-0.692946\pi$
$523$	−3.26644	+	1.88588i	−0.142831	+	0.0824638i	0.426881	+	0.904308i	$0.359612\pi$
$524$	−18.8495			−0.823446
$525$	1.32994	−	1.36573i	0.0580435	−	0.0596055i
$526$	−2.66717	−	2.66717i	−0.116294	−	0.116294i
$527$	18.0533	+	4.83738i	0.786416	+	0.210720i
$528$	−1.83193	+	0.490864i	−0.0797246	+	0.0213621i
$529$	24.5630	−	42.5443i	1.06796	−	1.84975i
$530$	−5.59121	−	9.68427i	−0.242867	−	0.420658i
$531$	9.51650	+	9.51650i	0.412981	+	0.412981i
$532$	0.955459	−	1.70684i	0.0414244	−	0.0740008i
$533$	0.192227	+	4.56387i	0.00832626	+	0.197683i
$534$	−1.67719	−	2.90498i	−0.0725791	−	0.125711i
$535$	0.406368	+	1.51659i	0.0175688	+	0.0655677i
$536$	4.45681	−	7.71942i	0.192505	−	0.333428i
$537$	4.09501	+	7.09276i	0.176713	+	0.306075i
$538$	13.9616	−	13.9616i	0.601929	−	0.601929i
$539$	−9.63337	−	9.13494i	−0.414939	−	0.393470i
$540$	−1.46279	+	1.46279i	−0.0629483	+	0.0629483i
$541$	6.85865	+	1.83777i	0.294876	+	0.0790119i	0.403224	−	0.915101i	$-0.367889\pi$
$541$	6.85865	+	1.83777i	0.294876	+	0.0790119i	−0.108348	+	0.994113i	$0.534556\pi$
$542$	17.7210	+	10.2312i	0.761180	+	0.439468i
$543$	−4.29637	−	2.48051i	−0.184375	−	0.106449i
$544$	−0.646025	+	2.41100i	−0.0276981	+	0.103371i
$545$	−30.9789			−1.32699
$546$	9.06359	−	2.97513i	0.387886	−	0.127324i
$547$	25.4103			1.08646			0.543232	−	0.839582i	$-0.317200\pi$
$547$	25.4103			1.08646			0.543232	+	0.839582i	$0.317200\pi$
$548$	4.32908	−	16.1564i	0.184929	−	0.690165i
$549$	8.23336	+	4.75353i	0.351391	+	0.202876i
$550$	1.18342	+	0.683246i	0.0504611	+	0.0291337i
$551$	−5.78798	−	1.55089i	−0.246576	−	0.0660699i
$552$	−6.00525	+	6.00525i	−0.255600	+	0.255600i
$553$	−17.7968	+	18.2757i	−0.756795	+	0.777160i
$554$	7.37679	−	7.37679i	0.313410	−	0.313410i
$555$	−3.17233	−	5.49464i	−0.134658	−	0.233234i
$556$	−8.15390	+	14.1230i	−0.345802	+	0.598947i
$557$	1.71305	+	6.39319i	0.0725843	+	0.270888i	0.992675	−	0.120818i	$-0.0385517\pi$
$557$	1.71305	+	6.39319i	0.0725843	+	0.270888i	−0.920090	+	0.391706i	$0.871885\pi$
$558$	−3.74396	−	6.48472i	−0.158494	−	0.274520i
$559$	−27.7631	−	25.5189i	−1.17426	−	1.07934i
$560$	4.70322	−	2.79930i	0.198747	−	0.118292i
$561$	3.34737	+	3.34737i	0.141326	+	0.141326i
$562$	−8.27074	−	14.3253i	−0.348880	−	0.604278i
$563$	−17.5835	+	30.4555i	−0.741057	+	1.28355i	0.210958	+	0.977495i	$0.432342\pi$
$563$	−17.5835	+	30.4555i	−0.741057	+	1.28355i	−0.952015	+	0.306053i	$0.900992\pi$
$564$	−1.80147	+	0.482703i	−0.0758557	+	0.0203255i
$565$	22.7764	+	6.10292i	0.958211	+	0.256752i
$566$	14.0573	+	14.0573i	0.590874	+	0.590874i
$567$	−2.56446	−	0.650785i	−0.107697	−	0.0273304i
$568$	−6.38258			−0.267807
$569$	−26.3141	+	15.1925i	−1.10315	+	0.636902i	−0.937046	−	0.349207i	$-0.886451\pi$
$569$	−26.3141	+	15.1925i	−1.10315	+	0.636902i	−0.166101	+	0.986109i	$0.553118\pi$
$570$	1.47732	−	0.395846i	0.0618781	−	0.0165802i
$571$	5.27769	+	3.04708i	0.220864	+	0.127516i	0.606350	−	0.795198i	$-0.292633\pi$
$571$	5.27769	+	3.04708i	0.220864	+	0.127516i	−0.385486	+	0.922714i	$0.625966\pi$
$572$	3.66524	+	5.77286i	0.153251	+	0.241375i
$573$			11.9765i			0.500326i
$574$	−2.33850	+	2.40143i	−0.0976072	+	0.100234i
$575$	6.11911			0.255184
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	2.87138	+	10.7161i	0.119537	+	0.446118i	0.999586	−	0.0287645i	$-0.00915729\pi$
$577$	2.87138	+	10.7161i	0.119537	+	0.446118i	−0.880049	+	0.474882i	$0.842491\pi$
$578$	−10.4028	+	2.78741i	−0.432698	+	0.115941i
$579$	−3.43795	+	12.8306i	−0.142876	+	0.533222i
$580$	−11.8558	−	11.8558i	−0.492284	−	0.492284i
$581$	5.34132	+	2.98998i	0.221595	+	0.124045i
$582$		−	1.53872i		−	0.0637821i
$583$	9.90260	+	2.65339i	0.410124	+	0.109892i
$584$	0.359224	−	0.622195i	0.0148648	−	0.0257466i
$585$	6.61071	+	3.45426i	0.273319	+	0.142816i
$586$	−11.7414	+	6.77887i	−0.485031	+	0.280033i
$587$	21.2423	−	21.2423i	0.876762	−	0.876762i	−0.116436	−	0.993198i	$-0.537147\pi$
$587$	21.2423	−	21.2423i	0.876762	−	0.876762i	0.993198	+	0.116436i	$0.0371471\pi$
$588$	6.15296	+	3.33783i	0.253744	+	0.137650i
$589$			5.53599i			0.228107i
$590$	7.20584	−	26.8925i	0.296660	−	1.10715i
$591$	−2.68776	−	10.0309i	−0.110560	−	0.412615i
$592$	0.793796	+	2.96249i	0.0326248	+	0.121757i
$593$	−2.11279	+	7.88502i	−0.0867617	+	0.323799i	−0.995642	−	0.0932580i	$-0.970272\pi$
$593$	−2.11279	+	7.88502i	−0.0867617	+	0.323799i	0.908880	+	0.417057i	$0.136939\pi$
$594$		−	1.89655i		−	0.0778166i
$595$	−11.9208	−	6.67308i	−0.488706	−	0.273570i
$596$	7.78401	−	7.78401i	0.318845	−	0.318845i
$597$	−1.35386	+	0.781653i	−0.0554099	+	0.0319909i
$598$	27.1393	+	14.1809i	1.10981	+	0.579901i
$599$	−3.39696	+	5.88370i	−0.138796	+	0.240401i	−0.927041	−	0.374960i	$-0.877657\pi$
$599$	−3.39696	+	5.88370i	−0.138796	+	0.240401i	0.788245	+	0.615361i	$0.210990\pi$
$600$	−0.695963	−	0.186483i	−0.0284126	−	0.00761312i
$601$		−	27.2049i		−	1.10971i	−0.831947	−	0.554856i	$-0.812773\pi$
$601$		−	27.2049i		−	1.10971i	0.831947	−	0.554856i	$-0.187227\pi$
$602$	−0.367336	−	27.6688i	−0.0149715	−	1.12770i
$603$	6.30288	+	6.30288i	0.256673	+	0.256673i
$604$	−5.43118	+	20.2695i	−0.220992	+	0.824752i
$605$	−14.7929	+	3.96374i	−0.601415	+	0.161149i
$606$	−1.08547	−	4.05104i	−0.0440943	−	0.164562i
$607$	−18.9113	+	10.9185i	−0.767588	+	0.443167i	−0.832013	−	0.554755i	$-0.812812\pi$
$607$	−18.9113	+	10.9185i	−0.767588	+	0.443167i	0.0644256	+	0.997923i	$0.479478\pi$
$608$	−0.739324			−0.0299835
$609$	5.27456	−	20.7848i	0.213736	−	0.842242i
$610$		−	19.6672i		−	0.796302i
$611$	3.60430	+	5.67688i	0.145814	+	0.229662i
$612$	−2.16164	−	1.24802i	−0.0873792	−	0.0504484i
$613$	24.5571	−	6.58005i	0.991851	−	0.265766i	0.273823	−	0.961780i	$-0.411712\pi$
$613$	24.5571	−	6.58005i	0.991851	−	0.265766i	0.718028	+	0.696014i	$0.245045\pi$
$614$	−26.3070	+	15.1884i	−1.06166	+	0.612952i
$615$	−2.62085			−0.105683
$616$	−1.23425	+	4.86365i	−0.0497293	+	0.195962i
$617$	15.2184	+	15.2184i	0.612670	+	0.612670i	0.943641	−	0.330971i	$-0.107376\pi$
$617$	15.2184	+	15.2184i	0.612670	+	0.612670i	−0.330971	+	0.943641i	$0.607376\pi$
$618$	5.42935	+	1.45479i	0.218401	+	0.0585203i
$619$	−36.8088	+	9.86290i	−1.47947	+	0.396423i	−0.906168	−	0.422919i	$-0.861006\pi$
$619$	−36.8088	+	9.86290i	−1.47947	+	0.396423i	−0.573305	+	0.819342i	$0.694339\pi$
$620$	−7.74509	+	13.4149i	−0.311050	+	0.538755i
$621$	−4.24635	−	7.35489i	−0.170400	−	0.295142i
$622$	−0.383074	−	0.383074i	−0.0153599	−	0.0153599i
$623$	−8.87407	+	0.117814i	−0.355532	+	0.00472011i
$624$	−2.65454	−	2.43996i	−0.106267	−	0.0976767i
$625$	−10.4391	−	18.0811i	−0.417566	−	0.723245i
$626$	−4.05820	−	15.1454i	−0.162198	−	0.605333i
$627$	−0.701084	+	1.21431i	−0.0279986	+	0.0484950i
$628$	−7.24646	−	12.5512i	−0.289165	−	0.500849i
$629$	5.41316	−	5.41316i	0.215837	−	0.215837i
$630$	1.48664	+	5.26748i	0.0592290	+	0.209861i
$631$	−15.3622	+	15.3622i	−0.611561	+	0.611561i	−0.943353	−	0.331792i	$-0.892347\pi$
$631$	−15.3622	+	15.3622i	−0.611561	+	0.611561i	0.331792	+	0.943353i	$0.392347\pi$
$632$	9.31308	+	2.49543i	0.370454	+	0.0992630i
$633$	−23.4222	−	13.5228i	−0.930948	−	0.537483i
$634$	−0.991566	−	0.572481i	−0.0393801	−	0.0227361i
$635$	5.58928	−	20.8595i	0.221804	−	0.827783i
$636$	−5.40555			−0.214344
$637$	4.84474	−	24.7695i	0.191955	−	0.981404i
$638$	15.3714			0.608561
$639$	1.65193	−	6.16510i	0.0653495	−	0.243887i
$640$	−1.79154	−	1.03435i	−0.0708168	−	0.0408861i
$641$	14.5601	+	8.40626i	0.575088	+	0.332027i	0.759179	−	0.650882i	$-0.225601\pi$
$641$	14.5601	+	8.40626i	0.575088	+	0.332027i	−0.184091	+	0.982909i	$0.558934\pi$
$642$	0.733114	+	0.196437i	0.0289337	+	0.00775276i
$643$	19.0614	−	19.0614i	0.751709	−	0.751709i	−0.223089	−	0.974798i	$-0.571614\pi$
$643$	19.0614	−	19.0614i	0.751709	−	0.751709i	0.974798	+	0.223089i	$0.0716141\pi$
$644$	6.10316	+	21.6248i	0.240498	+	0.852138i
$645$	15.2989	−	15.2989i	0.602393	−	0.602393i
$646$	0.922694	+	1.59815i	0.0363029	+	0.0628785i
$647$	−5.26682	+	9.12241i	−0.207060	+	0.358639i	−0.950787	−	0.309845i	$-0.899723\pi$
$647$	−5.26682	+	9.12241i	−0.207060	+	0.358639i	0.743727	+	0.668483i	$0.233056\pi$
$648$	0.258819	+	0.965926i	0.0101674	+	0.0379452i
$649$	12.7623	+	22.1049i	0.500962	+	0.867692i
$650$	0.109322	+	2.59555i	0.00428798	+	0.101806i
$651$	−19.8094	+	0.262993i	−0.776392	+	0.0103075i
$652$	11.8458	+	11.8458i	0.463919	+	0.463919i
$653$	20.6492	+	35.7655i	0.808066	+	1.39961i	0.914202	+	0.405259i	$0.132819\pi$
$653$	20.6492	+	35.7655i	0.808066	+	1.39961i	−0.106136	+	0.994352i	$0.533848\pi$
$654$	−7.48755	+	12.9688i	−0.292786	+	0.507121i
$655$	−37.6652	+	10.0924i	−1.47170	+	0.394341i
$656$	1.22374	+	0.327901i	0.0477791	+	0.0128024i
$657$	0.508020	+	0.508020i	0.0198197	+	0.0198197i
$658$	−1.21373	+	4.78278i	−0.0473160	+	0.186452i
$659$	4.37942			0.170598			0.0852990	−	0.996355i	$-0.472815\pi$
$659$	4.37942			0.170598			0.0852990	+	0.996355i	$0.472815\pi$
$660$	−3.39775	+	1.96169i	−0.132257	+	0.0763588i
$661$	26.3094	−	7.04959i	1.02332	−	0.274197i	0.292134	−	0.956377i	$-0.405635\pi$
$661$	26.3094	−	7.04959i	1.02332	−	0.274197i	0.731184	+	0.682180i	$0.238968\pi$
$662$	13.8839	+	8.01590i	0.539615	+	0.311547i
$663$	−1.96140	+	8.78330i	−0.0761743	+	0.341115i
$664$		−	2.31362i		−	0.0897857i
$665$	0.995332	−	3.92218i	0.0385973	−	0.152096i
$666$	−3.06699			−0.118844
$667$	59.6108	−	34.4163i	2.30814	−	1.33261i
$668$	−4.62198	−	17.2495i	−0.178830	−	0.667402i
$669$	−17.0675	+	4.57322i	−0.659867	+	0.176811i
$670$	4.77250	−	17.8112i	0.184378	−	0.688108i
$671$	12.7496	+	12.7496i	0.492193	+	0.492193i
$672$	−0.0351224	−	2.64552i	−0.00135487	−	0.102053i
$673$		−	16.9296i		−	0.652587i	−0.945268	−	0.326294i	$-0.894200\pi$
$673$		−	16.9296i		−	0.652587i	0.945268	−	0.326294i	$-0.105800\pi$
$674$	10.1218	+	2.71212i	0.389876	+	0.104467i
$675$	0.360257	−	0.623983i	0.0138663	−	0.0240171i
$676$	−5.53027	+	11.7650i	−0.212703	+	0.452501i
$677$	−38.3011	+	22.1132i	−1.47203	+	0.849878i	−0.999506	−	0.0314383i	$-0.989991\pi$
$677$	−38.3011	+	22.1132i	−1.47203	+	0.849878i	−0.472527	+	0.881316i	$0.656658\pi$
$678$	8.05992	−	8.05992i	0.309539	−	0.309539i
$679$	−3.55237	−	1.98856i	−0.136327	−	0.0763138i
$680$			5.16356i			0.198013i
$681$	4.90540	−	18.3072i	0.187975	−	0.701534i
$682$	−3.67555	−	13.7173i	−0.140744	−	0.525264i
$683$	0.367922	+	1.37310i	0.0140781	+	0.0525403i	0.972608	−	0.232453i	$-0.0746752\pi$
$683$	0.367922	+	1.37310i	0.0140781	+	0.0525403i	−0.958529	+	0.284993i	$0.908009\pi$
$684$	0.191351	−	0.714132i	0.00731649	−	0.0273055i
$685$		−	34.6015i		−	1.32206i
$686$	15.6576	−	9.89139i	0.597810	−	0.377655i
$687$	−6.03843	+	6.03843i	−0.230381	+	0.230381i
$688$	−9.05753	+	5.22937i	−0.345315	+	0.199368i
$689$	5.83215	+	18.5969i	0.222187	+	0.708487i
$690$	−8.78439	+	15.2150i	−0.334416	+	0.579226i
$691$	−35.2656	−	9.44939i	−1.34157	−	0.359472i	−0.484551	−	0.874763i	$-0.661017\pi$
$691$	−35.2656	−	9.44939i	−1.34157	−	0.359472i	−0.857015	+	0.515291i	$0.827684\pi$
$692$		−	4.90072i		−	0.186297i
$693$	−4.37847	−	2.45100i	−0.166324	−	0.0931057i
$694$	16.9696	+	16.9696i	0.644158	+	0.644158i
$695$	−8.73147	+	32.5863i	−0.331203	+	1.23607i
$696$	−7.82875	+	2.09771i	−0.296748	+	0.0795134i
$697$	−0.818457	−	3.05452i	−0.0310013	−	0.115698i
$698$	7.47196	−	4.31394i	0.282818	−	0.163285i
$699$	−12.8588			−0.486363
$700$	−1.32994	+	1.36573i	−0.0502672	+	0.0516198i
$701$		−	32.9830i		−	1.24575i	−0.782321	−	0.622876i	$-0.785964\pi$
$701$		−	32.9830i		−	1.24575i	0.782321	−	0.622876i	$-0.214036\pi$
$702$	3.04387	−	1.93258i	0.114883	−	0.0729405i
$703$	1.96371	+	1.13375i	0.0740628	+	0.0427602i
$704$	1.83193	−	0.490864i	0.0690435	−	0.0185001i
$705$	−3.34126	+	1.92908i	−0.125839	+	0.0726533i
$706$	−33.8416			−1.27365
$707$	−10.7552	−	2.72935i	−0.404491	−	0.102648i
$708$	−9.51650	−	9.51650i	−0.357652	−	0.357652i
$709$	−30.0344	−	8.04771i	−1.12797	−	0.302238i	−0.353864	−	0.935297i	$-0.615132\pi$
$709$	−30.0344	−	8.04771i	−1.12797	−	0.302238i	−0.774104	+	0.633059i	$0.781799\pi$
$710$	−12.7537	+	3.41734i	−0.478637	+	0.128250i
$711$	−4.82081	+	8.34988i	−0.180794	+	0.313145i
$712$	1.67719	+	2.90498i	0.0628553	+	0.108869i
$713$	−44.9668	−	44.9668i	−1.68402	−	1.68402i
$714$	−5.67483	+	3.37759i	−0.212375	+	0.126403i
$715$	10.4148	+	9.57292i	0.389491	+	0.358007i
$716$	−4.09501	−	7.09276i	−0.153038	−	0.265069i
$717$	4.08691	+	15.2526i	0.152628	+	0.569617i
$718$	16.0665	−	27.8280i	0.599597	−	1.03853i
$719$	−8.59059	−	14.8793i	−0.320375	−	0.554906i	0.660190	−	0.751098i	$-0.270476\pi$
$719$	−8.59059	−	14.8793i	−0.320375	−	0.554906i	−0.980565	+	0.196192i	$0.937142\pi$
$720$	1.46279	−	1.46279i	0.0545148	−	0.0545148i
$721$	10.3752	−	10.6544i	0.386392	−	0.396790i
$722$	13.0485	−	13.0485i	0.485616	−	0.485616i
$723$	3.08971	+	0.827886i	0.114908	+	0.0307894i
$724$	4.29637	+	2.48051i	0.159673	+	0.0921875i
$725$	5.05733	+	2.91985i	0.187825	+	0.108441i
$726$	−1.91606	+	7.15083i	−0.0711116	+	0.265392i
$727$	43.0733			1.59750			0.798751	−	0.601662i	$-0.205495\pi$
$727$	43.0733			1.59750			0.798751	+	0.601662i	$0.205495\pi$
$728$	−9.06359	+	2.97513i	−0.335919	+	0.110266i
$729$	−1.00000			−0.0370370
$730$	0.384670	−	1.43561i	0.0142373	−	0.0531342i
$731$	22.6080	+	13.0528i	0.836189	+	0.482774i
$732$	−8.23336	−	4.75353i	−0.304314	−	0.175696i
$733$	−6.94573	−	1.86110i	−0.256547	−	0.0687414i	0.128253	−	0.991741i	$-0.459063\pi$
$733$	−6.94573	−	1.86110i	−0.256547	−	0.0687414i	−0.384800	+	0.923000i	$0.625730\pi$
$734$	−9.61079	+	9.61079i	−0.354741	+	0.354741i
$735$	14.0820	+	3.37526i	0.519422	+	0.124498i
$736$	6.00525	−	6.00525i	0.221356	−	0.221356i
$737$	8.45258	+	14.6403i	0.311355	+	0.539282i
$738$	−0.633456	+	1.09718i	−0.0233178	+	0.0403877i
$739$	9.87132	+	36.8403i	0.363122	+	1.35519i	0.869948	+	0.493143i	$0.164152\pi$
$739$	9.87132	+	36.8403i	0.363122	+	1.35519i	−0.506826	+	0.862048i	$0.669181\pi$
$740$	3.17233	+	5.49464i	0.116617	+	0.201987i
$741$	−2.66331	+	0.112177i	−0.0978391	+	0.00412091i
$742$	−6.98583	+	12.4795i	−0.256458	+	0.458137i
$743$	−17.3632	−	17.3632i	−0.636994	−	0.636994i	0.312819	−	0.949813i	$-0.398727\pi$
$743$	−17.3632	−	17.3632i	−0.636994	−	0.636994i	−0.949813	+	0.312819i	$0.898727\pi$
$744$	3.74396	+	6.48472i	0.137260	+	0.237742i
$745$	11.3863	−	19.7217i	0.417163	−	0.722548i
$746$	27.2059	−	7.28981i	0.996080	−	0.266899i
$747$	2.23478	+	0.598808i	0.0817664	+	0.0219092i
$748$	−3.34737	−	3.34737i	−0.122392	−	0.122392i
$749$	1.40094	−	1.43864i	0.0511891	−	0.0525666i
$750$	−11.8340			−0.432116
$751$	−23.5978	+	13.6242i	−0.861097	+	0.497155i	−0.864380	−	0.502840i	$-0.832289\pi$
$751$	−23.5978	+	13.6242i	−0.861097	+	0.497155i	0.00328238	+	0.999995i	$0.498955\pi$
$752$	1.80147	−	0.482703i	0.0656930	−	0.0176024i
$753$	9.59919	+	5.54210i	0.349814	+	0.201965i
$754$	15.6634	+	24.6703i	0.570428	+	0.898440i
$755$			43.4104i			1.57987i
$756$	2.56446	+	0.650785i	0.0932687	+	0.0236688i
$757$	11.8716			0.431482			0.215741	−	0.976451i	$-0.430783\pi$
$757$	11.8716			0.431482			0.215741	+	0.976451i	$0.430783\pi$
$758$	−8.43777	+	4.87155i	−0.306474	+	0.176943i
$759$	−4.16876	−	15.5580i	−0.151317	−	0.564721i
$760$	−1.47732	+	0.395846i	−0.0535880	+	0.0143589i
$761$	−4.15900	+	15.5216i	−0.150764	+	0.562657i	0.848667	+	0.528927i	$0.177405\pi$
$761$	−4.15900	+	15.5216i	−0.150764	+	0.562657i	−0.999431	+	0.0337304i	$0.989261\pi$
$762$	−7.38157	−	7.38157i	−0.267406	−	0.267406i
$763$	20.2639	+	34.0463i	0.733604	+	1.23256i
$764$		−	11.9765i		−	0.433295i
$765$	−4.98761	−	1.33643i	−0.180327	−	0.0483186i
$766$	−8.72883	+	15.1188i	−0.315385	+	0.546263i
$767$	−22.4725	+	43.0075i	−0.811434	+	1.55291i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−23.9532	+	23.9532i	−0.863776	+	0.863776i	−0.991774	−	0.127999i	$-0.959145\pi$
$769$	−23.9532	+	23.9532i	−0.863776	+	0.863776i	0.127999	+	0.991774i	$0.459145\pi$
$770$	0.137799	+	10.3794i	0.00496592	+	0.374047i
$771$		−	6.47170i		−	0.233073i
$772$	3.43795	−	12.8306i	0.123735	−	0.461784i
$773$	−7.75055	−	28.9254i	−0.278768	−	1.04038i	−0.953274	−	0.302107i	$-0.902310\pi$
$773$	−7.75055	−	28.9254i	−0.278768	−	1.04038i	0.674506	−	0.738269i	$-0.264357\pi$
$774$	−2.70692	−	10.1024i	−0.0972983	−	0.363122i
$775$	1.39637	−	5.21131i	0.0501589	−	0.187196i
$776$			1.53872i			0.0552369i
$777$	−3.96360	+	7.08060i	−0.142193	+	0.254015i
$778$	10.0278	−	10.0278i	0.359515	−	0.359515i
$779$	0.811170	−	0.468329i	0.0290632	−	0.0167796i
$780$	−6.61071	−	3.45426i	−0.236701	−	0.123682i
$781$	6.05245	−	10.4832i	0.216574	−	0.375117i
$782$	−20.4759	−	5.48650i	−0.732216	−	0.196197i
$783$		−	8.10492i		−	0.289646i
$784$	−6.15296	−	3.33783i	−0.219749	−	0.119208i
$785$	−21.2001	−	21.2001i	−0.756662	−	0.756662i
$786$	−4.87862	+	18.2073i	−0.174015	+	0.649432i
$787$	39.0670	−	10.4680i	1.39259	−	0.373143i	0.516912	−	0.856039i	$-0.327082\pi$
$787$	39.0670	−	10.4680i	1.39259	−	0.373143i	0.875678	+	0.482895i	$0.160415\pi$
$788$	2.68776	+	10.0309i	0.0957477	+	0.357335i
$789$	−3.26660	+	1.88597i	−0.116294	+	0.0671425i
$790$	19.9455			0.709630
$791$	−8.19133	−	29.0237i	−0.291250	−	1.03196i
$792$			1.89655i			0.0673911i
$793$	−7.47066	+	33.4542i	−0.265291	+	1.18799i
$794$	−12.1975	−	7.04223i	−0.432873	−	0.249920i
$795$	−10.8014	+	2.89422i	−0.383086	+	0.102648i
$796$	1.35386	−	0.781653i	0.0479864	−	0.0277049i
$797$	−34.8869			−1.23576			−0.617878	−	0.786274i	$-0.712007\pi$
$797$	−34.8869			−1.23576			−0.617878	+	0.786274i	$0.712007\pi$
$798$	−1.40139	−	1.36466i	−0.0496086	−	0.0483086i
$799$	−3.29171	−	3.29171i	−0.116452	−	0.116452i
$800$	0.695963	+	0.186483i	0.0246060	+	0.00659316i
$801$	−3.24008	+	0.868177i	−0.114483	+	0.0306755i
$802$	−13.4892	+	23.3640i	−0.476322	+	0.825013i
$803$	0.681289	+	1.18003i	0.0240422	+	0.0416422i
$804$	−6.30288	−	6.30288i	−0.222285	−	0.222285i
$805$	23.7737	+	39.9431i	0.837911	+	1.40781i
$806$	18.2702	−	19.8770i	0.643542	−	0.700136i
$807$	−9.87236	−	17.0994i	−0.347524	−	0.601929i
$808$	1.08547	+	4.05104i	0.0381868	+	0.142515i
$809$	−4.40858	+	7.63588i	−0.154997	+	0.268463i	−0.933058	−	0.359726i	$-0.882870\pi$
$809$	−4.40858	+	7.63588i	−0.154997	+	0.268463i	0.778061	+	0.628189i	$0.216204\pi$
$810$	1.03435	+	1.79154i	0.0363432	+	0.0629483i
$811$	−19.6274	+	19.6274i	−0.689212	+	0.689212i	−0.962058	−	0.272846i	$-0.912035\pi$
$811$	−19.6274	+	19.6274i	−0.689212	+	0.689212i	0.272846	+	0.962058i	$0.412035\pi$
$812$	−5.27456	+	20.7848i	−0.185101	+	0.729403i
$813$	14.4691	−	14.4691i	0.507454	−	0.507454i
$814$	−5.61852	−	1.50548i	−0.196929	−	0.0527670i
$815$	30.0128	+	17.3279i	1.05130	+	0.606970i
$816$	2.16164	+	1.24802i	0.0756726	+	0.0436896i
$817$	−2.00129	+	7.46892i	−0.0700163	+	0.261304i
$818$	24.9842			0.873551
$819$	−0.527924	−	9.52477i	−0.0184472	−	0.332822i
$820$	2.62085			0.0915241
$821$	9.50562	−	35.4754i	0.331748	−	1.23810i	−0.575603	−	0.817729i	$-0.695233\pi$
$821$	9.50562	−	35.4754i	0.331748	−	1.23810i	0.907352	−	0.420373i	$-0.138101\pi$
$822$	−14.4854	−	8.36314i	−0.505236	−	0.291698i
$823$	5.73445	+	3.31079i	0.199890	+	0.115407i	0.596604	−	0.802536i	$-0.296516\pi$
$823$	5.73445	+	3.31079i	0.199890	+	0.115407i	−0.396714	+	0.917942i	$0.629850\pi$
$824$	−5.42935	−	1.45479i	−0.189141	−	0.0506800i
$825$	0.966256	−	0.966256i	0.0336407	−	0.0336407i
$826$	−34.2688	+	9.67167i	−1.19236	+	0.336520i
$827$	5.24742	−	5.24742i	0.182471	−	0.182471i	−0.609961	−	0.792432i	$-0.708815\pi$
$827$	5.24742	−	5.24742i	0.182471	−	0.182471i	0.792432	+	0.609961i	$0.208815\pi$
$828$	4.24635	+	7.35489i	0.147571	+	0.255600i
$829$	6.94513	−	12.0293i	0.241214	−	0.417795i	−0.719846	−	0.694134i	$-0.755788\pi$
$829$	6.94513	−	12.0293i	0.241214	−	0.417795i	0.961060	+	0.276338i	$0.0891210\pi$
$830$	−1.23875	−	4.62308i	−0.0429976	−	0.160469i
$831$	−5.21618	−	9.03468i	−0.180947	−	0.313410i
$832$	2.65454	+	2.43996i	0.0920296	+	0.0845905i
$833$	0.463850	+	17.4662i	0.0160714	+	0.605167i
$834$	11.5313	+	11.5313i	0.399298	+	0.399298i
$835$	−18.4713	−	31.9933i	−0.639227	−	1.10717i
$836$	0.701084	−	1.21431i	0.0242475	−	0.0419979i
$837$	−7.23277	+	1.93801i	−0.250001	+	0.0669876i
$838$	4.59545	+	1.23135i	0.158747	+	0.0425362i
$839$	0.975055	+	0.975055i	0.0336626	+	0.0336626i	0.723738	−	0.690075i	$-0.242423\pi$
$839$	0.975055	+	0.975055i	0.0336626	+	0.0336626i	−0.690075	+	0.723738i	$0.742423\pi$
$840$	−1.48664	−	5.26748i	−0.0512938	−	0.181745i
$841$	36.6898			1.26516
$842$	−10.9379	+	6.31500i	−0.376945	+	0.217629i
$843$	−15.9778	+	4.28125i	−0.550306	+	0.147454i
$844$	23.4222	+	13.5228i	0.806224	+	0.465474i
$845$	−4.75141	+	26.4699i	−0.163453	+	0.910593i
$846$			1.86502i			0.0641208i
$847$	14.0325	+	13.6648i	0.482164	+	0.469529i
$848$	5.40555			0.185627
$849$	17.2166	−	9.94003i	0.590874	−	0.341141i
$850$	−0.465470	−	1.73716i	−0.0159655	−	0.0595840i
$851$	−25.1595	+	6.74147i	−0.862457	+	0.231095i
$852$	−1.65193	+	6.16510i	−0.0565943	+	0.211213i
$853$	−2.36861	−	2.36861i	−0.0810996	−	0.0810996i	0.665393	−	0.746493i	$-0.268264\pi$
$853$	−2.36861	−	2.36861i	−0.0810996	−	0.0810996i	−0.746493	+	0.665393i	$0.768264\pi$
$854$	−21.6146	+	12.8647i	−0.739635	+	0.440222i
$855$		−	1.52943i		−	0.0523055i
$856$	−0.733114	−	0.196437i	−0.0250573	−	0.00671408i
$857$	−11.3833	+	19.7165i	−0.388847	+	0.673503i	−0.992295	−	0.123900i	$-0.960460\pi$
$857$	−11.3833	+	19.7165i	−0.388847	+	0.673503i	0.603448	+	0.797403i	$0.293793\pi$
$858$	6.52479	−	2.04622i	0.222753	−	0.0698570i
$859$	30.8712	−	17.8235i	1.05331	−	0.608130i	0.129737	−	0.991548i	$-0.458587\pi$
$859$	30.8712	−	17.8235i	1.05331	−	0.608130i	0.923575	+	0.383419i	$0.125253\pi$
$860$	−15.2989	+	15.2989i	−0.521688	+	0.521688i
$861$	1.71436	+	2.88036i	0.0584251	+	0.0981623i
$862$			6.01984i			0.205036i
$863$	−5.55709	+	20.7394i	−0.189166	+	0.705976i	0.804535	+	0.593906i	$0.202415\pi$
$863$	−5.55709	+	20.7394i	−0.189166	+	0.705976i	−0.993700	+	0.112070i	$0.964252\pi$
$864$	−0.258819	−	0.965926i	−0.00880520	−	0.0328615i
$865$	−2.62393	−	9.79263i	−0.0892162	−	0.332959i
$866$	−7.39412	+	27.5952i	−0.251263	+	0.937724i
$867$			10.7697i			0.365760i
$868$	19.8094	−	0.262993i	0.672375	−	0.00892657i
$869$	−12.9300	+	12.9300i	−0.438622	+	0.438622i
$870$	−14.5203	+	8.38329i	−0.492284	+	0.284220i
$871$	−14.8838	+	28.4843i	−0.504317	+	0.965155i
$872$	7.48755	−	12.9688i	0.253560	−	0.439179i
$873$	−1.48629	−	0.398251i	−0.0503034	−	0.0134787i
$874$		−	6.27886i		−	0.212385i
$875$	−15.2936	+	27.3205i	−0.517016	+	0.923601i
$876$	−0.508020	−	0.508020i	−0.0171644	−	0.0171644i
$877$	−5.00894	+	18.6936i	−0.169140	+	0.631239i	0.828336	+	0.560232i	$0.189288\pi$
$877$	−5.00894	+	18.6936i	−0.169140	+	0.631239i	−0.997476	+	0.0710071i	$0.977379\pi$
$878$	−2.34566	+	0.628518i	−0.0791622	+	0.0212114i
$879$	3.50900	+	13.0958i	0.118356	+	0.441710i
$880$	3.39775	−	1.96169i	0.114538	−	0.0661287i
$881$	−0.495142			−0.0166817			−0.00834087	−	0.999965i	$-0.502655\pi$
$881$	−0.495142			−0.0166817			−0.00834087	+	0.999965i	$0.502655\pi$
$882$	4.81660	−	5.07941i	0.162183	−	0.171033i
$883$		−	37.7485i		−	1.27034i	−0.772374	−	0.635168i	$-0.780931\pi$
$883$		−	37.7485i		−	1.27034i	0.772374	−	0.635168i	$-0.219069\pi$
$884$	1.96140	−	8.78330i	0.0659689	−	0.295414i
$885$	−24.1112	−	13.9206i	−0.810489	−	0.467936i
$886$	−19.7752	+	5.29876i	−0.664362	+	0.178015i
$887$	−42.2775	+	24.4089i	−1.41954	+	0.819572i	−0.996258	−	0.0864267i	$-0.972455\pi$
$887$	−42.2775	+	24.4089i	−1.41954	+	0.819572i	−0.423281	+	0.905998i	$0.639122\pi$
$888$	3.06699			0.102922
$889$	−26.5810	+	7.50193i	−0.891497	+	0.251607i
$890$	4.90674	+	4.90674i	0.164474	+	0.164474i
$891$	−1.83193	−	0.490864i	−0.0613720	−	0.0164446i
$892$	17.0675	−	4.57322i	0.571462	−	0.153123i
$893$	0.689428	−	1.19412i	0.0230708	−	0.0399598i
$894$	−5.50412	−	9.53342i	−0.184085	−	0.318845i
$895$	−11.9802	−	11.9802i	−0.400455	−	0.400455i
$896$	0.0351224	+	2.64552i	0.00117336	+	0.0883806i
$897$	20.7219	−	22.5442i	0.691883	−	0.752729i
$898$	16.9279	+	29.3199i	0.564890	+	0.978418i
$899$	−15.7075	−	58.6210i	−0.523873	−	1.95512i
$900$	−0.360257	+	0.623983i	−0.0120086	+	0.0207994i
$901$	−6.74626	−	11.6849i	−0.224751	−	0.389279i
$902$	−1.69901	+	1.69901i	−0.0565710	+	0.0565710i
$903$	−26.8211	−	6.80639i	−0.892549	−	0.226502i
$904$	−8.05992	+	8.05992i	−0.268069	+	0.268069i
$905$	9.91313	+	2.65621i	0.329524	+	0.0882956i
$906$	18.1731	+	10.4922i	0.603761	+	0.348581i
$907$	2.78754	+	1.60939i	0.0925589	+	0.0534389i	0.545565	−	0.838069i	$-0.316315\pi$
$907$	2.78754	+	1.60939i	0.0925589	+	0.0534389i	−0.453006	+	0.891507i	$0.649648\pi$
$908$	−4.90540	+	18.3072i	−0.162791	+	0.607546i
$909$	−4.19394			−0.139104
$910$	−16.5180	+	10.7977i	−0.547565	+	0.357941i
$911$	20.5603			0.681193			0.340597	−	0.940209i	$-0.389371\pi$
$911$	20.5603			0.681193			0.340597	+	0.940209i	$0.389371\pi$
$912$	−0.191351	+	0.714132i	−0.00633627	+	0.0236473i
$913$	3.80003	+	2.19395i	0.125763	+	0.0726091i
$914$	−16.4644	−	9.50570i	−0.544593	−	0.314421i
$915$	−18.9971	−	5.09024i	−0.628023	−	0.168278i
$916$	6.03843	−	6.03843i	0.199515	−	0.199515i
$917$	35.7293	+	34.7930i	1.17989	+	1.14897i
$918$	−1.76497	+	1.76497i	−0.0582528	+	0.0582528i
$919$	16.4951	+	28.5703i	0.544123	+	0.942448i	0.998662	+	0.0517211i	$0.0164707\pi$
$919$	16.4951	+	28.5703i	0.544123	+	0.942448i	−0.454539	+	0.890727i	$0.650196\pi$
$920$	8.78439	−	15.2150i	0.289613	−	0.501624i
$921$	7.86207	+	29.3417i	0.259064	+	0.966840i
$922$	−1.62938	−	2.82216i	−0.0536607	−	0.0929430i
$923$	22.9923	−	0.968419i	0.756802	−	0.0318759i
$924$	4.37847	+	2.45100i	0.144041	+	0.0806319i
$925$	−1.56257	−	1.56257i	−0.0513770	−	0.0513770i
$926$	−7.60122	−	13.1657i	−0.249792	−	0.432652i
$927$	2.81044	−	4.86783i	0.0923070	−	0.159880i
$928$	7.82875	−	2.09771i	0.256991	−	0.0688606i
$929$	−20.1071	−	5.38769i	−0.659693	−	0.176764i	−0.0865856	−	0.996244i	$-0.527596\pi$
$929$	−20.1071	−	5.38769i	−0.659693	−	0.176764i	−0.573108	+	0.819480i	$0.694262\pi$
$930$	10.9532	+	10.9532i	0.359170	+	0.359170i
$931$	−4.96160	+	1.47170i	−0.162610	+	0.0482329i
$932$	12.8588			0.421202
$933$	−0.469167	+	0.270874i	−0.0153599	+	0.00886801i
$934$	−7.42323	+	1.98905i	−0.242896	+	0.0650837i
$935$	−8.48096	−	4.89648i	−0.277357	−	0.160132i
$936$	−3.04387	+	1.93258i	−0.0994920	+	0.0631683i
$937$		−	9.29800i		−	0.303753i	−0.988400	−	0.151876i	$-0.951468\pi$
$937$		−	9.29800i		−	0.303753i	0.988400	−	0.151876i	$-0.0485315\pi$
$938$	−22.6966	+	6.40565i	−0.741071	+	0.209152i
$939$	−15.6797			−0.511688
$940$	3.34126	−	1.92908i	0.108980	−	0.0629196i
$941$	−0.848942	−	3.16829i	−0.0276747	−	0.103283i	0.950707	−	0.310091i	$-0.100359\pi$
$941$	−0.848942	−	3.16829i	−0.0276747	−	0.103283i	−0.978382	+	0.206807i	$0.933693\pi$
$942$	−13.9991	+	3.75105i	−0.456115	+	0.122216i
$943$	−2.78477	+	10.3929i	−0.0906844	+	0.338439i
$944$	9.51650	+	9.51650i	0.309736	+	0.309736i
$945$	5.47276	−	0.0726574i	0.178029	−	0.00236354i
$946$		−	19.8356i		−	0.644910i
$947$	27.1591	+	7.27725i	0.882551	+	0.236479i	0.671507	−	0.740998i	$-0.265647\pi$
$947$	27.1591	+	7.27725i	0.882551	+	0.236479i	0.211043	+	0.977477i	$0.432314\pi$
$948$	4.82081	−	8.34988i	0.156572	−	0.271191i
$949$	−1.19965	+	2.29587i	−0.0389423	+	0.0745272i
$950$	0.461325	−	0.266346i	0.0149674	−	0.00864142i
$951$	−0.809610	+	0.809610i	−0.0262534	+	0.0262534i
$952$	5.67483	−	3.37759i	0.183922	−	0.109468i
$953$		−	0.810435i		−	0.0262526i	−0.999914	−	0.0131263i	$-0.995822\pi$
$953$		−	0.810435i		−	0.0262526i	0.999914	−	0.0131263i	$-0.00417835\pi$
$954$	−1.39906	+	5.22136i	−0.0452963	+	0.169048i
$955$	−6.41243	−	23.9315i	−0.207501	−	0.774405i
$956$	−4.08691	−	15.2526i	−0.132180	−	0.493303i
$957$	3.97842	−	14.8477i	0.128604	−	0.479957i
$958$		−	19.7724i		−	0.638818i
$959$	−38.0276	+	22.6336i	−1.22798	+	0.730877i
$960$	−1.46279	+	1.46279i	−0.0472112	+	0.0472112i
$961$	−21.7103	+	12.5344i	−0.700331	+	0.404336i
$962$	−3.30903	−	10.5515i	−0.106687	−	0.340194i
$963$	0.379487	−	0.657292i	0.0122288	−	0.0211809i
$964$	−3.08971	−	0.827886i	−0.0995130	−	0.0266644i
$965$		−	27.4789i		−	0.884578i
$966$	22.4676	−	0.298284i	0.722883	−	0.00959712i
$967$	−0.150065	−	0.150065i	−0.00482576	−	0.00482576i	0.704690	−	0.709516i	$-0.251086\pi$
$967$	−0.150065	−	0.150065i	−0.00482576	−	0.00482576i	−0.709516	+	0.704690i	$0.751086\pi$
$968$	1.91606	−	7.15083i	0.0615845	−	0.229836i
$969$	1.78251	−	0.477622i	0.0572624	−	0.0153434i
$970$	0.823858	+	3.07468i	0.0264525	+	0.0987221i
$971$	−10.7495	+	6.20622i	−0.344968	+	0.199167i	−0.662467	−	0.749091i	$-0.730490\pi$
$971$	−10.7495	+	6.20622i	−0.344968	+	0.199167i	0.317499	+	0.948259i	$0.397157\pi$
$972$	1.00000			0.0320750
$973$	41.5243	−	11.7194i	1.33121	−	0.375706i
$974$			25.7940i			0.826492i
$975$	2.53540	+	0.566180i	0.0811978	+	0.0181323i
$976$	8.23336	+	4.75353i	0.263544	+	0.152157i
$977$	−40.4126	+	10.8285i	−1.29291	+	0.346435i	−0.838767	−	0.544491i	$-0.816723\pi$
$977$	−40.4126	+	10.8285i	−1.29291	+	0.346435i	−0.454147	+	0.890927i	$0.650056\pi$
$978$	14.5081	−	8.37627i	0.463919	−	0.267844i
$979$	−6.36176			−0.203323
$980$	−14.0820	−	3.37526i	−0.449833	−	0.107819i
$981$	10.5890	+	10.5890i	0.338081	+	0.338081i
$982$	−30.8046	−	8.25406i	−0.983014	−	0.263398i
$983$	15.9691	−	4.27890i	0.509335	−	0.136476i	0.00500575	−	0.999987i	$-0.498407\pi$
$983$	15.9691	−	4.27890i	0.509335	−	0.136476i	0.504329	+	0.863512i	$0.331740\pi$
$984$	0.633456	−	1.09718i	0.0201938	−	0.0349768i
$985$	10.7414	+	18.6046i	0.342249	+	0.592793i
$986$	−14.3050	−	14.3050i	−0.455563	−	0.455563i
$987$	4.30568	+	2.41025i	0.137051	+	0.0767190i
$988$	2.66331	−	0.112177i	0.0847311	−	0.00356881i
$989$	−44.4115	−	76.9229i	−1.41220	−	2.44601i
$990$	1.01545	+	3.78970i	0.0322730	+	0.120445i
$991$	21.8253	−	37.8026i	0.693305	−	1.20084i	−0.277444	−	0.960742i	$-0.589487\pi$
$991$	21.8253	−	37.8026i	0.693305	−	1.20084i	0.970749	−	0.240097i	$-0.0771793\pi$
$992$	−3.74396	−	6.48472i	−0.118871	−	0.205890i
$993$	11.3362	−	11.3362i	0.359743	−	0.359743i
$994$	12.0982	+	11.7811i	0.383731	+	0.373675i
$995$	2.28678	−	2.28678i	0.0724958	−	0.0724958i
$996$	−2.23478	−	0.598808i	−0.0708118	−	0.0189740i
$997$	−14.0983	−	8.13966i	−0.446498	−	0.257786i	0.259852	−	0.965648i	$-0.416326\pi$
$997$	−14.0983	−	8.13966i	−0.446498	−	0.257786i	−0.706350	+	0.707863i	$0.749660\pi$
$998$	−11.7735	−	6.79745i	−0.372685	−	0.215170i
$999$	−0.793796	+	2.96249i	−0.0251146	+	0.0937289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.73.2	yes	40
7.5	odd	6		546.2.bz.a.229.7	yes	40
13.5	odd	4		546.2.bz.a.31.7	✓	40
91.5	even	12	inner	546.2.bz.b.187.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.31.7	✓	40	13.5	odd	4
546.2.bz.a.229.7	yes	40	7.5	odd	6
546.2.bz.b.73.2	yes	40	1.1	even	1	trivial
546.2.bz.b.187.2	yes	40	91.5	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99820 - 0.535417i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.718636 + 2.54628i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.99820 - 0.535417i) q^{5} +(-0.707107 + 0.707107i) q^{6} +(0.718636 + 2.54628i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.03435 - 1.79154i) q^{10} +(0.490864 + 1.83193i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-2.43996 + 2.65454i) q^{13} +(-2.64552 + 0.0351224i) q^{14} +(-1.46279 - 1.46279i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.24802 - 2.16164i) q^{17} +(-0.965926 + 0.258819i) q^{18} +(0.714132 + 0.191351i) q^{19} +(1.46279 + 1.46279i) q^{20} +(-0.650785 + 2.56446i) q^{21} -1.89655 q^{22} +(-7.35489 + 4.24635i) q^{23} +(0.965926 - 0.258819i) q^{24} +(-0.623983 - 0.360257i) q^{25} +(-1.93258 - 3.04387i) q^{26} +1.00000i q^{27} +(0.650785 - 2.56446i) q^{28} -8.10492 q^{29} +(1.79154 - 1.03435i) q^{30} +(1.93801 + 7.23277i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(-0.490864 + 1.83193i) q^{33} +(1.76497 + 1.76497i) q^{34} +(-0.0726574 - 5.47276i) q^{35} -1.00000i q^{36} +(2.96249 + 0.793796i) q^{37} +(-0.369662 + 0.640273i) q^{38} +(-3.44034 + 1.07892i) q^{39} +(-1.79154 + 1.03435i) q^{40} +(0.895842 - 0.895842i) q^{41} +(-2.30865 - 1.29234i) q^{42} +10.4587i q^{43} +(0.490864 - 1.83193i) q^{44} +(-0.535417 - 1.99820i) q^{45} +(-2.19807 - 8.20332i) q^{46} +(0.482703 - 1.80147i) q^{47} +1.00000i q^{48} +(-5.96712 + 3.65970i) q^{49} +(0.509480 - 0.509480i) q^{50} +(2.16164 - 1.24802i) q^{51} +(3.44034 - 1.07892i) q^{52} +(2.70278 - 4.68135i) q^{53} +(-0.965926 - 0.258819i) q^{54} -3.92339i q^{55} +(2.30865 + 1.29234i) q^{56} +(0.522781 + 0.522781i) q^{57} +(2.09771 - 7.82875i) q^{58} +(12.9998 - 3.48328i) q^{59} +(0.535417 + 1.99820i) q^{60} +(8.23336 - 4.75353i) q^{61} -7.48791 q^{62} +(-1.84583 + 1.89550i) q^{63} -1.00000i q^{64} +(6.29683 - 3.99791i) q^{65} +(-1.64246 - 0.948277i) q^{66} +(8.60990 - 2.30701i) q^{67} +(-2.16164 + 1.24802i) q^{68} -8.49270 q^{69} +(5.30509 + 1.34627i) q^{70} +(-4.51316 - 4.51316i) q^{71} +(0.965926 + 0.258819i) q^{72} +(0.693968 - 0.185948i) q^{73} +(-1.53350 + 2.65609i) q^{74} +(-0.360257 - 0.623983i) q^{75} +(-0.522781 - 0.522781i) q^{76} +(-4.31186 + 2.56637i) q^{77} +(-0.151729 - 3.60236i) q^{78} +(4.82081 + 8.34988i) q^{79} +(-0.535417 - 1.99820i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.633456 + 1.09718i) q^{82} +(1.63597 - 1.63597i) q^{83} +(1.84583 - 1.89550i) q^{84} +(-3.65119 + 3.65119i) q^{85} +(-10.1024 - 2.70692i) q^{86} +(-7.01907 - 4.05246i) q^{87} +(1.64246 + 0.948277i) q^{88} +(-0.868177 + 3.24008i) q^{89} +2.06869 q^{90} +(-8.51266 - 4.30519i) q^{91} +8.49270 q^{92} +(-1.93801 + 7.23277i) q^{93} +(1.61516 + 0.932511i) q^{94} +(-1.32453 - 0.764717i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(-1.08804 + 1.08804i) q^{97} +(-1.99060 - 6.71100i) q^{98} +(-1.34107 + 1.34107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Introduction

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